2019-2020/1ST/Derivation/Nombre_derive/4E_fonction_derivee.tex

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\documentclass[a5paper,10pt]{article}
\usepackage{myXsim}
\title{Fonctions dérivée}
\tribe{1ST}
\date{Janvier 2020}
\pagestyle{empty}
\setlength{\mathindent}{0cm}
\geometry{left=5mm,right=10mm, bottom=8mm, top=5mm}
\begin{document}
\begin{exercise}[subtitle={Une fonction dérivée?}]
\begin{enumerate}[wide]
\item $f(x) = 2x^2$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-1,ymax=9,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{2*x**2}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $f'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
f'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $g(x) = -4x$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.35, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-7,ymax=7,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{-4*x}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $g'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
g'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $h(x) = 2x^2-4x+1$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-2,xmax=3,xstep=1,
ymin=-1,ymax=10,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{2*x**2-4*x+1}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $h'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
h'(x) &=&
\end{flalign*}
\end{minipage}
\end{enumerate}
\end{exercise}
\clearpage
\begin{exercise}[subtitle={Une fonction dérivée?}]
\begin{enumerate}[wide]
\item $f(x) = -2x^2$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-9,ymax=1,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{-2*x**2}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $f'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
f'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $g(x) = 3x$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.35, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-7,ymax=7,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{3*x}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $g'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
g'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $h(x) = -2x^2+3x+1$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-2,xmax=3,xstep=1,
ymin=-10,ymax=1,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{-2*x**2+3*x-1}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $h'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
h'(x) &=&
\end{flalign*}
\end{minipage}
\end{enumerate}
\end{exercise}
\clearpage
\begin{exercise}[subtitle={Une fonction dérivée?}]
\begin{enumerate}[wide]
\item $f(x) = 8x^2$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-1,ymax=20,ystep=2]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{4*x**2}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $f'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
f'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $g(x) = -6x$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.35, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-14,ymax=14,ystep=2]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{-3*x}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $g'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
g'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $h(x) = 8x^2-6x+10$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-2,xmax=3,xstep=1,
ymin=-1,ymax=20,ystep=2]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{4*x**2-3*x+5}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $h'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
h'(x) &=&
\end{flalign*}
\end{minipage}
\end{enumerate}
\end{exercise}
\clearpage
\begin{exercise}[subtitle={Une fonction dérivée?}]
\begin{enumerate}[wide]
\item $f(x) = -0.5x^2$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.8, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-6,ymax=1,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{-0.5*x**2}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $f'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
f'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $g(x) = 2x$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.35, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-7,ymax=7,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{2*x}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $g'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
g'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $h(x) = -0.5x^2+2x+1$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-2,xmax=4,xstep=1,
ymin=-8,ymax=2,ystep=1]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:4, line width=1pt]{-0.5*x**2+2*x-1}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $h'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
h'(x) &=&
\end{flalign*}
\end{minipage}
\end{enumerate}
\end{exercise}
\clearpage
\begin{exercise}[subtitle={Une fonction dérivée?}]
\begin{enumerate}[wide]
\item $f(x) = 50x^2$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.8, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-5,ymax=50,ystep=10]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{5*x**2}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $f'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
f'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $g(x) = -100x$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.35, xscale=1]
\tkzInit[xmin=-3,xmax=3,xstep=1,
ymin=-300,ymax=300,ystep=50]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:3, line width=1pt]{-100*x}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $g'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
g'(x) &=&
\end{flalign*}
\end{minipage}
\vfill
\item $h(x) = 50x^2-100x+20$
\begin{minipage}{0.6\textwidth}
\begin{tikzpicture}[yscale=.45, xscale=1]
\tkzInit[xmin=-2,xmax=4,xstep=1,
ymin=-40,ymax=200,ystep=20]
\tkzGrid
\tkzAxeXY[up space=0.5,right space=.5]
\tkzFct[domain = -3:4, line width=1pt]{50*x**2-100*x+20}
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}{0.4\textwidth}
\begin{tabular}{|m{1cm}|c|}
\hline
x & Nombre dérivé $h'(x)$\\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{tabular}
Fonction dérivée:
\begin{flalign*}
h'(x) &=&
\end{flalign*}
\end{minipage}
\end{enumerate}
\end{exercise}
\end{document}