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