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\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} %%% Local Variables: