128 lines
3.5 KiB
TeX
128 lines
3.5 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\usepackage{pgfplots}
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\pgfplotsset{compat = newest}
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\tikzexternalize
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\author{Benjamin Bertrand}
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\title{Fonctions tableaux - Cours \hfill (suite)}
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\date{2023-01-10}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\bigskip
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\setcounter{section}{2}
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\section{Les variations d'une fonction}
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\begin{definition}[ Variations d'une fonction ]
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Soit $f$ une fonction définie sur un intervalle $I$.
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\medskip
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\begin{minipage}{0.5\linewidth}
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On dit que $f$ est \textbf{croissante} sur $I$ si et seulement \dotfill
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\medskip
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\\.\dotfill
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\medskip
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\\.\dotfill
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\medskip
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\end{minipage}
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\hfill
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\begin{minipage}{0.4\linewidth}
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\begin{tikzpicture}[scale=0.6]
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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xmin=0, xmax=2.5,
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xticklabel=\empty,
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ylabel = {$y$},
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yticklabel=\empty,
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ymin=0, ymax=5,
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legend pos = north west,
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]
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\addplot[domain=1:2,samples=30, color=red, very thick]{x*x};
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\end{axis}
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\end{tikzpicture}
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\end{minipage}
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\begin{minipage}{0.5\linewidth}
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On dit que $f$ est \textbf{décroissante} sur $I$ si et seulement \dotfill
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\medskip
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\\.\dotfill
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\medskip
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\\.\dotfill
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\medskip
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\end{minipage}
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\hfill
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\begin{minipage}{0.4\linewidth}
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\begin{tikzpicture}[scale=0.6]
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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xmin=0, xmax=2.5,
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xticklabel=\empty,
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ylabel = {$y$},
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yticklabel=\empty,
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ymin=0, ymax=5,
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legend pos = north west,
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]
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\addplot[domain=1:2,samples=30, color=red, very thick]{5 - x*x};
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\end{axis}
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\end{tikzpicture}
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\end{minipage}
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\end{definition}
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\begin{definition}[Monotone]
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Une fonction $f$ est dite \textbf{monotone} sur un intervalle $I$ si et seulement si elle ne change pas de variations sur cet intervalle.
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\end{definition}
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\begin{definition}[ Extremum d'une fonction ]
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Soit $f$ une fonction définie sur un intervalle $I$.
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\medskip
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\begin{minipage}{0.5\linewidth}
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On dit que $f$ a pour maximum $M$ sur l'intervalle $I$ si et seulement si
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\medskip
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\\.\dotfill
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\medskip
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\\.\dotfill
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\medskip
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On dit que $f$ a pour minimum $m$ sur l'intervalle $I$ si et seulement si
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\medskip
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\\.\dotfill
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\medskip
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\\.\dotfill
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\medskip
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\end{minipage}
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\hfill
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\begin{minipage}{0.4\linewidth}
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\begin{tikzpicture}
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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xticklabel=\empty,
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ylabel = {$y$},
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yticklabel=\empty,
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legend pos = north west,
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]
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\addplot[domain=-0.8:0.8,samples=30, color=red, very thick]{x*(x-1)*(x+1)};
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\end{axis}
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\end{tikzpicture}
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\end{minipage}
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\end{definition}
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\end{document}
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