\exercice[style=A,N=1,verif]{Nombre d\'eriv\'e}
\begin{tikzpicture}[scale=1.5,baseline=-1.7cm]
\draw[gray!20] (-2,-3) grid (5,1);
\draw (-2,-3) rectangle (5,1);
\clip (-2,-3) rectangle (5,1);
\draw[->,>=stealth'] (-2,0) -- (5,0);
\draw[->,>=stealth'] (0,-3) -- (0,1);
\draw[purple] plot[domain=-2:5,samples=70] (\x,{\x*exp(-\x)});
\draw[green!50!black] plot[domain=-2:5,samples=70] (\x,{\x});
\draw[violet] plot[domain=-2:5] (\x,{\x*\x/2-2*\x});
\draw[red] (-2,-2) -- (5,-2) node[below left] {${\cal T}_1$};
\draw (-.1,-1) -- (.1,-1) node[right] {-1};
\node[above right,purple] at (-1,-3) {$\mathcal{C}_f$};
\node[below right,violet] at (4.3,1) {$\mathcal{C}_g$};
\node[above right,green!50!black] at (-2,-1.8) {$\mathcal{T}$};
\end{tikzpicture}
\hfill
\begin{minipage}{\dimexpr\linewidth-11cm}
\begin{itemize}
\item $\color{green!50!black}\mathcal{T}$ est la tangente \`a $\mathcal{C}_f$ au point d'abscisse 0.
\item $\color{red}{\cal T}_1$ est la tangente \`a ${\cal C}_g$ au point d'abscisse 2.
\item ${\cal C}_g$ et ${\cal C}_f$ se coupent en deux points d'abscisses respectives 0 et 4.
\end{itemize}

\`A l'aide du graphique ci-dessus, r\'epondez aux questions suivantes.
\end{minipage}

\begin{enumerate}
\item Que vaut $f'(0)$ ? $g'(2)$ ?
\item R\'esoudre l'in\'equation $f(x) \geqslant g(x)$ sur $\intervFF{-2}{5}$.
\end{enumerate}
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