From c86f17a2eb871f7a8aa76ff852a2d2abf6e9f5f1 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 10 Jan 2023 14:59:09 +0100 Subject: [PATCH] =?UTF-8?q?Feat(1ST):=20Bilan=20sur=20la=20fonction=20d?= =?UTF-8?q?=C3=A9riv=C3=A9e?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../1B_fonction_derivee.pdf | Bin 0 -> 23789 bytes .../1B_fonction_derivee.tex | 46 ++++++++++++++++++ .../2B_variations_min_max.pdf | Bin 0 -> 23622 bytes .../2B_variations_min_max.tex | 31 ++++++++++++ 1ST/05_Fonction_derivee/index.rst | 12 ++++- 5 files changed, 88 insertions(+), 1 deletion(-) create mode 100644 1ST/05_Fonction_derivee/1B_fonction_derivee.pdf create mode 100644 1ST/05_Fonction_derivee/1B_fonction_derivee.tex create mode 100644 1ST/05_Fonction_derivee/2B_variations_min_max.pdf create mode 100644 1ST/05_Fonction_derivee/2B_variations_min_max.tex diff --git a/1ST/05_Fonction_derivee/1B_fonction_derivee.pdf 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On appelle cette fonction \textbf{fonction dérivée de $f$} et on la note $f'$. + +Pour calculer une fonction dérivée, on pourra utiliser le formulaire suivant: + +\begin{propriete}[Tableau des dérivées] +\begin{center} + \begin{tabular}{|m{4cm}|m{4cm}|} + \hline + Fonction $f$ & Fonction dérivée $f'$ \\ + \hline + $a$ & $0$ \\ + \hline + $ax$ & $a$ \\ + \hline + $ax^2$ & $2ax$ \\ + \hline + $ax^3$ & $3ax^2$\\ + \hline + \end{tabular} +\end{center} +\end{propriete} + +\subsection*{Exemple} + +On veut calculer la fonction dérivée de $f(x) = 2x^2 + 3x + 1$ +\begin{flalign*} + f'(x) &=& +\end{flalign*} + +\afaire{Dériver la fonction} + +\end{document} diff --git a/1ST/05_Fonction_derivee/2B_variations_min_max.pdf b/1ST/05_Fonction_derivee/2B_variations_min_max.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a148cf61d2a59a5c7c1662ac60049c2a85156f3b GIT binary patch literal 23622 zcmce-1#DzXvMp+6W@fh;%FJxHnVFfHnW4?h%*@Qp%*@PgGql~W&wc;?IbU})dU{_o 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zb+JYMnb+Ia5$Ej=Fj~Avc2a3C0Sgd+C#gWl^NnAyrk%z^~m8AXC z(A#s`4Dy>^aa)+kenpi!X%#+-LgTq!WY!^V)t>N`Mo7tiOeKt$>xs6ktw@#@1w#fg zR_+@LeinLD_}>|g9V{8m#y!t&ZZ+!8-Qi~|NMxBDf5+=L?hQ(b1-Bp)J9%lPT}iyx zmbMT1_f_u9kEba49syZysnX XceD>Bm7^CEr>s-b^YW@`KcxQ`zt>TU literal 0 HcmV?d00001 diff --git a/1ST/05_Fonction_derivee/2B_variations_min_max.tex b/1ST/05_Fonction_derivee/2B_variations_min_max.tex new file mode 100644 index 0000000..852de61 --- /dev/null +++ b/1ST/05_Fonction_derivee/2B_variations_min_max.tex @@ -0,0 +1,31 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + + +\title{Nombre dérivé - Nombre dérivé} +\tribe{1ST} +\date{Janvier 2023} + +\pagestyle{empty} + +%\geometry{left=15mm,right=15mm, bottom=8mm, top=5mm} +\begin{document} + +\setcounter{section}{1} +\section{Variation de la fonction} + +Connaître la dérivée et étudier son signe permet de connaître les variations de la fonction. + +\begin{propriete}[Lien entre fonction et dérivée] + Soit $f$ une fonction dérivable sur un intervalle $I$ et $f'$ sa dérivée. + \begin{itemize} + \item Si $f'(x) > 0$ (positif) pour tout $x$ dans $I$, alors $f$ est croissante sur $I$. + \item Si $f'(x) < 0$ (négatif) pour tout $x$ dans $I$, alors $f$ est décroissante sur $I$. + \end{itemize} +\end{propriete} + +\subsection*{Exemple} +Étude des variations de la fonction $f(x) = -4x^2 + 5x -1$ +\afaire{Dériver $f$ puis tracer le tableau de variations} + +\end{document} diff --git a/1ST/05_Fonction_derivee/index.rst b/1ST/05_Fonction_derivee/index.rst index b357af3..f47d33e 100644 --- a/1ST/05_Fonction_derivee/index.rst +++ b/1ST/05_Fonction_derivee/index.rst @@ -2,7 +2,7 @@ Fonction dérivée ################ :date: 2023-01-04 -:modified: 2023-01-05 +:modified: 2023-01-10 :authors: Benjamin Bertrand :tags: Dérivation :category: 1ST @@ -58,6 +58,11 @@ Enfin, en groupe, ils vont devoir chercher une méthode pour calculer des foncti Bilan: notion de fonction dérivée et les formules. +.. image:: ./1B_fonction_derivee.pdf + :height: 200px + :alt: Formulaire sur les fonctions dérivées + + Exercices techniques de dérivation. Étape 2: Calculs de fonctions dérivées @@ -67,6 +72,11 @@ Utilisation le formulaire pour calculer des fonctions dérivées, puis calcul de Bilan: Étude de signe d'une fonction pour en déduire les variations. +.. image:: ./2B_variations_min_max.pdf + :height: 200px + :alt: Lien entre le signe de la dérivée et la croissance de la fonction + + Étape 3: Étude de variations de fonctions -----------------------------------------