From 6f39b401d9001f0172e8e21ed40e2466c5391442 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 30 Sep 2025 17:43:38 +0200 Subject: [PATCH] =?UTF-8?q?feat(tstmg):=20fin=20de=20la=20s=C3=A9quence=20?= =?UTF-8?q?sur=20la=20d=C3=A9rivation?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Tstmg/04_Derivation_polynomes/1B.tex | 14 --- Tstmg/04_Derivation_polynomes/1B_tableaux.pdf | Bin 0 -> 17835 bytes Tstmg/04_Derivation_polynomes/1B_tableaux.tex | 94 ++++++++++++++++++ .../04_Derivation_polynomes/2B_derivation.pdf | Bin 0 -> 19191 bytes .../04_Derivation_polynomes/2B_derivation.tex | 72 ++++++++++++++ Tstmg/04_Derivation_polynomes/index.rst | 26 ++++- 6 files changed, 188 insertions(+), 18 deletions(-) delete mode 100644 Tstmg/04_Derivation_polynomes/1B.tex create mode 100644 Tstmg/04_Derivation_polynomes/1B_tableaux.pdf create mode 100644 Tstmg/04_Derivation_polynomes/1B_tableaux.tex create mode 100644 Tstmg/04_Derivation_polynomes/2B_derivation.pdf create mode 100644 Tstmg/04_Derivation_polynomes/2B_derivation.tex diff --git a/Tstmg/04_Derivation_polynomes/1B.tex b/Tstmg/04_Derivation_polynomes/1B.tex deleted file mode 100644 index d782b87..0000000 --- a/Tstmg/04_Derivation_polynomes/1B.tex +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass[a4paper,10pt]{article} -\usepackage{myXsim} - -\author{Benjamin Bertrand} -\title{Dérivation polynomes - Cours} -\date{octobre 2025} - -\pagestyle{empty} - -\begin{document} - -\maketitle - -\end{document} diff --git a/Tstmg/04_Derivation_polynomes/1B_tableaux.pdf b/Tstmg/04_Derivation_polynomes/1B_tableaux.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5c706b49c630fd604d87af93f8eb4867eb9b7414 GIT binary patch literal 17835 zcmch91yH0-vLNoR1A{c~?(XjH?(Xg|z+i*BySu~SHn_XH%izv2yZ3JYi?{dQi;LLp z=>EF8GW)B_uIx%L5_w@!8U|W67?QF1p1Fagss2G2W&l0F&d?Hun;Sr<>|t*Lpi`GK zv@|ht2GA+F7&`y0N7T;I20-`c`Zo*)0G*(qojXA5^Q-g#2Kv9hbO3ZR2F{KafBG5z 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+\usepackage{pgfplots} +\pgfplotsset{compat = newest} + + +\author{Benjamin Bertrand} +\title{Dérivation polynomes - Cours} +\date{octobre 2025} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\section{Tableaux de signes} + +Ce type de tableau représentera uniquement le \textbf{signe} de la fonction ainsi que les valeurs où elle est \textbf{nulle}. + +\paragraph{Exemple}: + +\begin{minipage}{0.3\linewidth} + \begin{tikzpicture}[scale=0.7] + % {0.1*(x+4)*(x+1)*(x-5)} + \begin{axis}[ + axis lines = center, + grid = both, + xlabel = {$x$}, + xtick distance=1, + ylabel = {$y$}, + ytick distance=2, + legend pos = north west, + legend entries={$f(x)$} + ] + \addplot[domain=-6:6,samples=40, color=red, very thick]{0.1*(x+4)*(x+1)*(x-5)}; + \end{axis} + \end{tikzpicture} +\end{minipage} +\hfill +\begin{minipage}{0.6\linewidth} + Tableau de signe de la fonction $f$ + + \begin{center} + \begin{tikzpicture} + \tkzTabInit[lgt=1,espcl=2] + {$x$/1, $f(x)$/2} + {$-6$, , , , $6$} + \tkzTabLine{, , , , } + \end{tikzpicture} + \end{center} + +\end{minipage} + +\section{Tableaux de variations} + +Ce type de tableau représentera uniquement les \textbf{variations} de la fonction. + +\paragraph{Exemple}: + +\begin{minipage}{0.3\linewidth} + \begin{tikzpicture}[scale=0.7] + % x sin(2x) + \begin{axis}[ + axis lines = center, + grid = both, + xlabel = {$x$}, + xtick distance=1, + ylabel = {$y$}, + ytick distance=1, + legend pos = north west, + ] + \addplot[domain=-6:6,samples=40, color=red, very thick]{x*sin(deg(x))}; + \end{axis} + \end{tikzpicture} + +\end{minipage} +\hfill +\begin{minipage}{0.6\linewidth} + Tableau de variations de la fonction $f$ + + \begin{center} + \begin{tikzpicture} + \tkzTabInit[lgt=1,espcl=2] + {$x$/1, $f(x)$/2} + {$-6$, , , , $6$} + \tkzTabVar{, , , , } + \end{tikzpicture} + \end{center} +\end{minipage} + +\afaire{Compléter les tableaux de signes et de variations} + +\end{document} diff --git a/Tstmg/04_Derivation_polynomes/2B_derivation.pdf 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hEe_Lv=b?k6p1q^%m#qsy$I3$YmFJ2`NJbdqe*x) 0$ (positif - "+") pour tout $x$ dans $I$, alors $f$ est croissante ($\nearrow$) sur $I$. + \item Si $f'(x) < 0$ (négatif - "-") pour tout $x$ dans $I$, alors $f$ est décroissante ($\searrow$) sur $I$. + \end{itemize} +\end{propriete} + +L'étude des variations d'une fonction se fera alors en suivant les étapes suivantes +\begin{enumerate} + \item Dériver la fonction $f(x)$ pour connaître $f'(x)$ + \item Étudier le signe de $f'(x)$ en résolvant l'inéquation $f'(x) > 0$ + \item Reporter le signe de $f'(x)$ dans un tableau de signe. + \item Déduire les variations de $f(x)$ grace à la propriété précédente. +\end{enumerate} + + +\subsection*{Exemple} +Étude des variations de la fonction $f(x) = -4x^2 + 5x -1$ +\afaire{Suivre les étapes pour étudier les variations} + + +\end{document} diff --git a/Tstmg/04_Derivation_polynomes/index.rst b/Tstmg/04_Derivation_polynomes/index.rst index 5fd7071..0498c22 100644 --- a/Tstmg/04_Derivation_polynomes/index.rst +++ b/Tstmg/04_Derivation_polynomes/index.rst @@ -32,11 +32,29 @@ Capacités attendues Progression =========== +Pour ce chapitre de "révisions" , on suivra une démarche explicite en montrant la méthode grace au cours puis en laissant les élèves reproduire la méthode en exercices. + +.. image:: ./plan_de_travail.pdf + :height: 200px + :alt: Plan de travail + + Étape 1: Va et viens entre graphique et les tableaux ---------------------------------------------------- -Étape 2: Dérivation -------------------- +Bilan sur les tableaux -Étape 3: Etude des variations d'un polynôme -------------------------------------------- + +.. image:: ./1B_tableaux.pdf + :height: 200px + :alt: Bilan sur les tableaux + + +Étape 2: Dérivation et étude des variations d'un polynôme +--------------------------------------------------------- + +Bilan sur la dérivation + +.. image:: ./2B_derivation.pdf + :height: 200px + :alt: Bilan sur la dérivation