{"id":268814,"date":"2024-02-12T09:00:00","date_gmt":"2024-02-12T08:00:00","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=268814"},"modified":"2024-02-10T15:17:23","modified_gmt":"2024-02-10T14:17:23","slug":"theoreme-valeurs-intermediaires","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/theoreme-valeurs-intermediaires\/","title":{"rendered":"Le th\u00e9or\u00e8me des valeurs interm\u00e9diaires (TVI) : cours et exercices \ud83d\udcc9"},"content":{"rendered":"\n<p>Si tu fais des math\u00e9matiques en Terminale, ne bouge pas ! Notre fiche de cours devrait t\u2019int\u00e9resser. On te parle d\u2019un des th\u00e9or\u00e8mes les plus importants \u00e0 conna\u00eetre pour le bac : <strong>le th\u00e9or\u00e8me des valeurs interm\u00e9diaires<\/strong> (ou TVI pour les intimes), un concept cl\u00e9 qui permet d&#8217;explorer les <strong>variations d&#8217;une fonction continue sur un intervalle donn\u00e9<\/strong>. Donc accroche-toi bien et c\u2019est parti ! \ud83c\udfa2<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/C0QuQM4RUegareij1k\/giphy.gif\" alt=\"Des montagnes russes. \" \/><figcaption class=\"wp-element-caption\"><em>Ce moment o\u00f9 tu es bien content que la courbe soit continue<\/em><\/figcaption><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\">Le th\u00e9or\u00e8me des valeurs interm\u00e9diaires, c\u2019est quoi ?&nbsp;\ud83d\udc40<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">D\u00e9finition&nbsp;\ud83d\udcd6<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Th\u00e9or\u00e8me \ud83d\udcdc<\/h4>\n\n\n<p>Soit <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> une fonction continue sur un intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> et soient <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/> deux r\u00e9els de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<br \/>\nPour tout r\u00e9el k compris entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-21bfcad32dddd87d1f10c4d55bc920e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-fc96bbb86e6f4df31fcd5eb119a28631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"\/>, il existe au moins un r\u00e9el <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> compris entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/> tel que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-53eca4d67c9161481507ea0ad044dc82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#99;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/>.<\/p>\n\n\n<p>Autrement dit, quand on a un nombre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-21bfcad32dddd87d1f10c4d55bc920e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-fc96bbb86e6f4df31fcd5eb119a28631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"\/>, alors il existe au moins un ant\u00e9c\u00e9dent au nombre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<br \/>\nIl existe au moins un nombre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> de l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-66dab9378074ff1620ffe294dd0d26b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#97;&#44;&#98;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -5px;\"\/> tel que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-53eca4d67c9161481507ea0ad044dc82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#99;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Graphique \ud83d\udcc8<\/h4>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1920\" height=\"1396\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?func=bound&amp;w=1024&amp;h=1024\" alt=\"\" class=\"wp-image-268815\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=1920 1920w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=1024 1024w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=768 768w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=1536 1536w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=172 172w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=374 374w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=510 510w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=384 384w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=209 209w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI-1.png?w=1080 1080w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/figure>\n\n\n<p>Ici, <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> est bien compris entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-21bfcad32dddd87d1f10c4d55bc920e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-fc96bbb86e6f4df31fcd5eb119a28631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"\/> et il existe 3 ant\u00e9c\u00e9dents dans notre cas de figure : <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-31a707843a3de0e8b273be5a643c76e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>, <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-89910718eaec9f5ccef3eda8d0669e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-69fa1eb3c737005f82719a095a15e06e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\"\/> !<\/p>\n\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 Rappel<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p>Comme son nom l\u2019indique, une fonction continue est une fonction dont la courbe ne fait aucun saut. Tu ne l\u00e8ves pas la main quand tu traces la courbe.<\/p>\n\n        <\/div>\n              <\/section>\n\n\n<section class=\"relance\">\n        <div >\n                            <a  href=\"https:\/\/sherpas.com\/cours\/maths\/online\">\n                    <div class=\"relance__container\"\n                        >\n                        \n                                                        <picture>\n                            <source srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-1.jpg\" media=\"(min-width: 999px)\">\n                            <source srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-1.jpg\" media=\"(max-width: 999px)\">\n                                <img decoding=\"async\"\n                                    src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/07\/relance-cours-particulier-1.jpg\"\n                                    alt=\"Personne qui donne des cours particuliers\"\n                                >\n                            <\/picture>\n                                                <div class=\"relance__content\">\n                            \n                                <div class=\"relance__title\"> <p>Si tu as des lacunes en maths, prends des cours particuliers en ligne avec un de nos Sherpas ! <\/p>\n<\/div>\n                                                        <button type=\"button\"\n                                    class=\"relance__button btn btn-white\">\n                                Le premier cours est gratuit !\n                            <\/button>\n                        <\/div>\n                    <\/div>\n                <\/a>\n                    <\/div>\n    <\/section>\n\n    \n\n\n<h3 class=\"wp-block-heading\">Cas particulier \u261d\ufe0f<\/h3>\n\n\n\n<p>Prenons le cas particulier d\u2019une <strong>fonction continue strictement monotone<\/strong>, c\u2019est-\u00e0-dire soit strictement croissante, soit strictement d\u00e9croissante. C\u2019est le <strong>corollaire<\/strong> au th\u00e9or\u00e8me des valeurs interm\u00e9diaires, qu\u2019on l\u2019appelle \u00e9galement le <strong>th\u00e9or\u00e8me de bijection<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Avant de te le pr\u00e9senter, voici un rappel de ce que sont une fonction monotone et une fonction non monotone.&nbsp;<\/p>\n\n\n\n<p>\u21aa\ufe0f Exemple fonction monotone d\u00e9croissante&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1920\" height=\"1396\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?func=bound&amp;w=1024&amp;h=1024\" alt=\"\" class=\"wp-image-268816\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=1920 1920w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=1024 1024w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=768 768w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=1536 1536w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=172 172w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=374 374w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=510 510w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=384 384w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=209 209w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/courbe-decroissante-monotone-.png?w=1080 1080w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/figure>\n\n\n\n<p>\u21aa\ufe0f Exemple fonction monotone croissante&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1920\" height=\"1396\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?func=bound&amp;w=1024&amp;h=1024\" alt=\"\" class=\"wp-image-268817\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=1920 1920w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=1024 1024w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=768 768w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=1536 1536w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=172 172w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=374 374w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=510 510w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=384 384w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=209 209w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/fonction-monotone-croissante.png?w=1080 1080w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/figure>\n\n\n\n<p>\u21aa\ufe0f Exemple d\u2019une fonction non monotone&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1920\" height=\"1396\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?func=bound&amp;w=1024&amp;h=1024\" alt=\"\" class=\"wp-image-268818\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=1920 1920w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=1024 1024w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=768 768w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=1536 1536w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=172 172w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=374 374w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=510 510w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=384 384w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=209 209w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/focntion-non-monotone-.png?w=1080 1080w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Corollaire (TVI appliqu\u00e9 aux fonctions strictement monotones)<\/h4>\n\n\n<p>Soit <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> une fonction continue et strictement monotone sur <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-295b606df26ce6ef86b49aa75cd58531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#97;&#44;&#98;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"31\" style=\"vertical-align: -5px;\"\/>.<br \/>\nPour tout r\u00e9el <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> compris entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-21bfcad32dddd87d1f10c4d55bc920e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-fc96bbb86e6f4df31fcd5eb119a28631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"\/>, il existe un <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-464c97f567a4bd67fcbfa2c8b45d20a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#98;&#102;&#123;&#117;&#110;&#105;&#113;&#117;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -4px;\"\/> r\u00e9el <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-d60bff48780225f6c3cee6c87c3e80bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#105;&#110;&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#97;&#44;&#98;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -5px;\"\/> tel que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-53eca4d67c9161481507ea0ad044dc82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#99;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n\n<p>Dans ce cas particulier, il y a donc un seul ant\u00e9c\u00e9dent !&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Graphique \ud83d\udcc9<\/h4>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1920\" height=\"1396\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?func=bound&amp;w=1024&amp;h=1024\" alt=\"\" class=\"wp-image-268819\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=1920 1920w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=1024 1024w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=768 768w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=1536 1536w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=172 172w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=374 374w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=510 510w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=384 384w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=209 209w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/TVI2.png?w=1080 1080w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/figure>\n\n\n<p>Dans ce cas, notre fonction est strictement croissante. On a bien <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> compris entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-21bfcad32dddd87d1f10c4d55bc920e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-fc96bbb86e6f4df31fcd5eb119a28631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"\/> et nous avons un unique ant\u00e9c\u00e9dent c tel que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-53eca4d67c9161481507ea0ad044dc82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#99;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/>.<\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zaWdudXA9dHJ1ZQ==\" data-banner=\"2\" data-name=\"Cours part&amp;#8217; global #1 = CPG1\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Antoine2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Antoine<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">18\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Bastien2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Bastien<\/p>                          <p class=\"push__teachers-school\">Polytechnique<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Olivier2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Olivier<\/p>                          <p class=\"push__teachers-school\">La Sorbonne<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">13\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/David2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">David<\/p>                          <p class=\"push__teachers-school\">EDHEC<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">25\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Jeanne2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Jeanne<\/p>                          <p class=\"push__teachers-school\">Aix-Marseille Universit\u00e9<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Emilie2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Emilie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Lyon<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Agathe2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Agathe<\/p>                          <p class=\"push__teachers-school\">ENS Lyon<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Ton premier cours particulier est offert ! <span role=\"img\" aria-label=\"\ud83c\udf81\">\ud83c\udf81<\/span><!-- notionvc: 91b6b7d7-50f2-46f4-ae1f-ecbabe834aad --><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos profs sont pass\u00e9s par les meilleures \u00e9coles et universit\u00e9s.<!-- notionvc: 21bb66b6-b36d-4ce8-8950-173722d75a1e --><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: #ffffff; border-color: ; background-color: \"\n\n                                    >\n                                        J&#8217;EN PROFITE MAINTENANT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">M\u00e9thode d\u2019application du TVI et de son corollaire&nbsp;\ud83e\udd13<\/h2>\n\n\n\n<p>Tu peux avoir plusieurs types de questions en exercices.&nbsp;&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/yNs2a0jRkYxy6191B2\/giphy.gif\" alt=\"Un homme prend des notes. \" \/><figcaption class=\"wp-element-caption\"><em>Prends bien note ! <\/em><\/figcaption><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">Question sur le TVI&nbsp;\u2753<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u00c9nonc\u00e9<\/h4>\n\n\n<p>D\u00e9montrer que l\u2019\u00e9quation <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-252f9958e223f77bf50cb3b92a7c3e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/> admet au moins une solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">M\u00e9thode&nbsp;<\/h4>\n\n\n<p>1. Tu v\u00e9rifies que la fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> est continue sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n<p>2. Tu trouves a et b sur l\u2019intervalle I tel que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-26ea93d87b74cf58cc79a25c2522226e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"\/><br \/>\ncar comme la fonction est continue, elle va prendre toutes les valeurs interm\u00e9diaires entre <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-21bfcad32dddd87d1f10c4d55bc920e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-fc96bbb86e6f4df31fcd5eb119a28631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"\/>. Et donc elle va prendre la valeur k. <\/p>\n<p>3. Tu conclus : d\u2019apr\u00e8s le th\u00e9or\u00e8me des valeurs interm\u00e9diaires, f(x)=k admet au moins une solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Question sur le corollaire du TVI \u2753<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u00c9nonc\u00e9<\/h4>\n\n\n<p>D\u00e9montrer que l\u2019\u00e9quation <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-252f9958e223f77bf50cb3b92a7c3e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/> admet exactement une solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">M\u00e9thode<\/h4>\n\n\n<p>1. Tu v\u00e9rifies que la fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> est continue sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n\n\n\n<p>2. Tu fais un tableau de variations \u00e0 l\u2019aide de la <a href=\"https:\/\/sherpas.com\/blog\/derivee-dune-fonction\/\">d\u00e9riv\u00e9e<\/a>.<\/p>\n\n\n<p>3. Tu conclus : d\u2019apr\u00e8s le corollaire du th\u00e9or\u00e8me des valeurs interm\u00e9diaires, l\u2019\u00e9quation <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-252f9958e223f77bf50cb3b92a7c3e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/> admet exactement une solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/p>\n\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9wcm9mZXNzZXVycz9zaWdudXA9dHJ1ZQ==\" data-banner=\"2\" data-name=\"Cours part&amp;#8217; global #2 = CPG2\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Thibault2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Thibault<\/p>                          <p class=\"push__teachers-school\">ENS Paris Ulm<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Sophie2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Sophie<\/p>                          <p class=\"push__teachers-school\">Sciences Po Bordeaux<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">12\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Noemie2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">No\u00e9mie<\/p>                          <p class=\"push__teachers-school\">M2 en droit \u00e0 Assas<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Fanny2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fanny<\/p>                          <p class=\"push__teachers-school\">Ponts ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Simon2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Simon<\/p>                          <p class=\"push__teachers-school\">4e ann\u00e9e de m\u00e9decine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2022\/01\/Victor2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Victor<\/p>                          <p class=\"push__teachers-school\">ESCP<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">25\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Besoin d&#8217;un prof particulier ? <span role=\"img\" aria-label=\"\u2728\">\u2728<\/span><!-- notionvc: 9b5ed38b-ea2e-4d3c-a3bb-f0091c2eedd2 --><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos profs sont l\u00e0 pour t&#8217;aider \u00e0 progresser !<\/p>\n<p>&nbsp;<\/p>\n<p><!-- notionvc: 20490bdd-6579-484b-9d99-0ff0bc1aa8e7 --><\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        JE PRENDS UN COURS GRATUIT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\">Exercices \u270d\ufe0f<\/h2>\n\n\n\n<p>On esp\u00e8re que tu as bien retenu les \u00e9tapes, car maintenant c\u2019est \u00e0 toi de les appliquer !<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/l378bl7lVJ1XAMRFu\/giphy.gif\" alt=\"Une femme qui que tu fais des maths. \" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">Exercice 1&nbsp;<\/h3>\n\n\n<p>Soit la fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-e3c371e201c0afd51b542793145ff889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#120;&#94;&#50;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"107\" style=\"vertical-align: -5px;\"\/><\/p>\n<p>D\u00e9montre que l\u2019\u00e9quation <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-0bce6c022ed0fc63f4659af75888f96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/> admet au moins une solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5d22c22741545ab31af5c32d8def210e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#49;&#59;&#51;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exercice 2<\/h3>\n\n\n<p>Soit <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-7908bc46969871d121f654b517830aba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#120;&#94;&#50;&#45;&#54;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"\/> <\/p>\n<p>Montre qu\u2019il existe sur unique solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-e71c71d5a045d514381bc64aa61231a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#52;&#59;&#54;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -5px;\"\/> pour <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-288f7c17c09c261515cbaa5af9d62df2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Corrig\u00e9s<strong>&nbsp;<\/strong>\ud83d\udcaf<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Corrig\u00e9 1<\/h3>\n\n\n<p>1. On v\u00e9rifie que la fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> est continue sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>La fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-e3c371e201c0afd51b542793145ff889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#120;&#94;&#50;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"107\" style=\"vertical-align: -5px;\"\/> est un polyn\u00f4me.<\/p>\n\n\n\n<p>Les <a href=\"https:\/\/sherpas.com\/blog\/degre-d-un-polynome\/\">polyn\u00f4mes<\/a> sont continus sur l\u2019ensemble des r\u00e9els.&nbsp;<\/p>\n\n\n<p>La fonction est donc continue sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5d22c22741545ab31af5c32d8def210e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#49;&#59;&#51;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n<p>2. On trouve <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/> sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> tel que <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-26ea93d87b74cf58cc79a25c2522226e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#97;&#41;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"\/><br \/>\n<img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-aded5a96cddfe5f42b2df3b3e7660b6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#49;&#41;&#61;&#49;&#94;&#50;&#45;&#52;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" style=\"vertical-align: -5px;\"\/><br \/>\n<img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-2dac3b65edeb837046faf7baed387a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#51;&#41;&#61;&#51;&#94;&#50;&#45;&#52;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-afccb34ebff231995b5498780db0a19e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#49;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> et <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-810099b49518841a7e097e000c44b5f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#51;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -5px;\"\/> sont de signes oppos\u00e9s, le th\u00e9or\u00e8me des valeurs interm\u00e9diaires garantit l&#8217;existence d&#8217;au moins une solution <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> dans l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-eca1c81e883c49c5d09fcae99f1730a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#49;&#59;&#51;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -5px;\"\/> tel que<br \/>\n<img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-68a9b035283a46cb37132d982264d8b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#99;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/>.<\/p>\n\n\n<p>3. On conclut.  <\/p>\n<p>D\u2019apr\u00e8s le th\u00e9or\u00e8me des valeurs interm\u00e9diaires, <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-e3c371e201c0afd51b542793145ff889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#120;&#94;&#50;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"107\" style=\"vertical-align: -5px;\"\/> admet au moins une solution sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-5d22c22741545ab31af5c32d8def210e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#49;&#59;&#51;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Corrig\u00e9 2&nbsp;<\/h3>\n\n\n<p>1. On v\u00e9rifie que la fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> est continue sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>. <\/p>\n<p>La fonction <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-7908bc46969871d121f654b517830aba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#120;&#94;&#50;&#45;&#54;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"147\" style=\"vertical-align: -5px;\"\/> est un polyn\u00f4me et les polyn\u00f4mes sont continus sur l\u2019ensemble des r\u00e9els. La fonction est donc continue sur l\u2019intervalle.<\/p>\n\n\n<p>2. On fait un tableau de variations<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-c41a1b6b04f98f9e01e301fef27cf6e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#61;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-1ac10a271e8d021f5c97afbcacc04845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/> quand <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"\/> et est n\u00e9gatif de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-e9e2bbc70bd377a579163ca907e1c2fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#92;&#105;&#110;&#102;&#116;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"30\" style=\"vertical-align: 0px;\"\/> \u00e0 <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>, puis positif de <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> \u00e0 <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-48164f38d81657b64512ac914fe52dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#123;&#92;&#105;&#110;&#102;&#116;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -2px;\"\/><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1104\" height=\"244\" src=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?func=bound&amp;w=1024&amp;h=244\" alt=\"\" class=\"wp-image-268850\" style=\"width:698px;height:auto\" srcset=\"https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=1104 1104w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=300 300w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=1024 1024w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=768 768w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=200 200w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=396 396w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=288 288w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=610 610w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=265 265w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=60 60w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=320 320w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=576 576w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=940 940w, https:\/\/adymrxvmro.cloudimg.io\/v7\/sherpas.com\/content\/uploads\/2023\/12\/tableau-de-variations-TVI.png?w=1080 1080w\" sizes=\"(max-width: 1104px) 100vw, 1104px\" \/><\/figure><\/div>\n\n<p>Pour l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-1496e93dc1d0a3a01022f25c3241e4e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#40;&#52;&#44;&#55;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-c41a1b6b04f98f9e01e301fef27cf6e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#61;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"\/><br \/>\n<img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-83a9988e94959df7ec9b5f5b3994e890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#52;&#41;&#61;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#52;&#45;&#54;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"\/><br \/>\n<img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-468cd74eb48a8bf19dc25138f5a0e274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#54;&#41;&#61;&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#54;&#45;&#54;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" style=\"vertical-align: -5px;\"\/><\/p>\n<p>On sait que sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-61e5e41ea1eb405cb0e7ed9a43597715_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#40;&#52;&#59;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"\/> la fonction est strictement croissante. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-d7cf00f770db6e886f9caec9fa20585b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#52;&#41;&#61;&#52;&#94;&#50;&#45;&#54;&#92;&#116;&#105;&#109;&#101;&#115;&#52;&#43;&#57;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"197\" style=\"vertical-align: -5px;\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-0ca3d61c26339f94478130807bf5499d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#54;&#41;&#61;&#54;&#94;&#50;&#45;&#54;&#92;&#116;&#105;&#109;&#101;&#115;&#54;&#43;&#57;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-78839d05aef08db19c675e9b33932a55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#52;&#41;&#61;&#49;&#60;&#52;&#60;&#57;&#61;&#102;&#40;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"187\" style=\"vertical-align: -5px;\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-288f7c17c09c261515cbaa5af9d62df2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/> est bien compris dans l\u2019intervalle.<\/p>\n\n\n<p>3. On conclut.<br \/>\nD\u2019apr\u00e8s le corollaire du th\u00e9or\u00e8me des valeurs interm\u00e9diaires, comme la fonction est strictement croissante sur l\u2019intervalle <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-3d9ad7760058ead254d2d2603aa09b81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#98;&#114;&#97;&#99;&#107;&#123;&#52;&#59;&#54;&#125;&#92;&#114;&#98;&#114;&#97;&#99;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -5px;\"\/>, alors l\u2019\u00e9quation <img decoding=\"async\" src=\"https:\/\/sherpas.com\/content\/ql-cache\/quicklatex.com-288f7c17c09c261515cbaa5af9d62df2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/> admet exactement une solution sur cet intervalle.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/26u4lOMA8JKSnL9Uk\/giphy.gif\" alt=\"Bob l'\u00e9ponge qui se frotte les mains pour avoir terminer une t\u00e2che. \" \/><\/figure><\/div>\n\n\n<p>Voil\u00e0 ! Notre fiche de math\u00e9matiques sur le <strong>th\u00e9or\u00e8me des valeurs interm\u00e9diaires<\/strong> touche \u00e0 sa fin. On esp\u00e8re qu\u2019elle t\u2019aura aid\u00e9 \u00e0 mieux comprendre et \u00e0 appliquer ce th\u00e9or\u00e8me tr\u00e8s important. Si tu as encore des difficult\u00e9s ou que tu veux exceller en maths, prends des <a href=\"https:\/\/sherpas.com\/cours\/maths\">cours particuliers<\/a> avec un Sherpa !<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;268814&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;6&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;4.7&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Tu as aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;4.7\\\/5 - (6 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Le th\u00e9or\u00e8me des valeurs interm\u00e9diaires (TVI) : cours et exercices \ud83d\udcc9&quot;,&quot;width&quot;:&quot;133.8&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 133.8px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            4.7\/5 - (6 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Si tu fais des math\u00e9matiques en Terminale, ne bouge pas ! Notre fiche de cours devrait t\u2019int\u00e9resser. On (&#8230;)<\/p>\n","protected":false},"author":332,"featured_media":268853,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[803,810],"tag":[770],"class_list":["post-268814","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-fiche-revision"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/268814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/332"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=268814"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/268814\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/268853"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=268814"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=268814"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=268814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}