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Bertrand Benjamin 2018-09-07 15:47:12 +02:00
parent b9c34518cc
commit cf87c92af3
2 changed files with 69 additions and 1 deletions
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PreStSauveur/TESL/Polynomes_derivation/T2_tlb_varia_sgn.pdf
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PreStSauveur/TESL/Polynomes_derivation/T2_tlb_varia_sgn.tex
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@ -13,7 +13,7 @@
\hspace{-1cm}
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}[scale=0.8]
\begin{tikzpicture}[scale=0.5]
\repere{-5}{5}{-5}{5}
\draw[very thick, color=red] plot [smooth,tension=0.5, mark=*] coordinates{(-4, 4) (-3.5, 2) (-3, 0) (-2, 1) (-1, 0) (0, -2) (1, -3) (2, -2) (2.5,0) (3, 2) (4, 3)};
\draw (4,3) node[above right] {$\mathcal{C}_f$};
@ -34,6 +34,74 @@
\tkzTabVar{+/ 4, -/ 0, +/ 1, -/ -3, +/ 3}
\end{tikzpicture}
\end{minipage}
\begin{exercise}[subtitle={Tableaux}]
Tracer le tableau de variation et le tableau de signe des fonctions représentées ci-dessous.
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}[scale=0.6, baseline=(a.north)]
\repere{-5}{5}{-5}{5}
\draw[very thick, color=red] plot [smooth,tension=0.5, mark=*] coordinates{(-4, -2) (-3.5, -3) (-3, 0) (-2, 1) (-1, 0) (0, -2) (1, -1) (2, -2) (2.5,0) (3, 2) (4, 3)};
\draw (4,3) node[above right] {$\mathcal{C}_f$};
\end{tikzpicture}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}[baseline=(a.north), yscale=0.7, xscale=1.3]
\tkzInit[xmin=-0.2,xmax=0.2,xstep=.1,
ymin=-12,ymax=6,ystep=2]
\tkzGrid
\tkzAxeXY
\draw (-1,3) node[below left] {$\mathcal{C}_g$};
\tkzFct[domain = -.1:.2,color=red,very thick]%
{-5+x*(0.5+4*x*(x*(-2+x*1)))}
\end{tikzpicture}
\end{minipage}
\end{exercise}
\begin{exercise}[subtitle={Graphique}]
Pour chaque tableau ci-dessous, tracer le graphique d'une fonction qui pourrait convenir.
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}[baseline=(a.north)]
\tkzTabInit[lgt=1,espcl=1]{$x$/1,$f(x)$/1}{-10, -3, -2 , -1, 6, 10}
\tkzTabLine{,+, z, -, z, +, z, -, z, +, }
\end{tikzpicture}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}[baseline=(a.north)]
\tkzTabInit[lgt=1,espcl=1]{$x$/1,$g(x)$/1}{$-\infty$, -2, 1, 4, $+\infty$}
\tkzTabLine{,+, z, -, z, -, z, -, }
\end{tikzpicture}
\end{minipage}
\begin{tikzpicture}[baseline=(a.north)]
\tkzTabInit[lgt=1,espcl=2]{$x$/1,$f(x)$/1}{-5, -3, 0, 3, $+\infty$}
\tkzTabVar{+/ 2, -/ -2, +/ -1, -/ -3, +/ }
\end{tikzpicture}
\end{exercise}
\begin{exercise}[subtitle={Signe de la dérivée et variations de la fonction}]
Compléter les tableaux de signe et de variations suivants
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}
\tkzTabInit[lgt=3,espcl=1.5]{$x$/1,$x-3$/1,$2x+6$/1,$(x-3)(2x+6)$/1}{-10, -3, 3, 10}
\tkzTabLine{}
\tkzTabLine{}
\tkzTabLine{}
\end{tikzpicture}
\end{minipage}
\begin{minipage}{0.5\textwidth}
\begin{tikzpicture}
\tkzTabInit[lgt=1,espcl=1.5]{$x$/1,$f'(x)$/1, $f(x)$/2}{-15, -10 , -3, 2, 10}
\tkzTabLine{,+, z, -, z, +, z, -, }
\tkzTabVar{}
\end{tikzpicture}
avec $f(x) = \dfrac{x^4}{4} + \dfrac{11x^3}{3} + 2x^2 - 60x$
\end{minipage}
\end{exercise}
\end{document}
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