\begin{center}
\begin{tikzpicture}
\node[inner sep = 0pt, outer sep = 0pt] (tab) {
\begin{tikzpicture}[scale=1.5]
\filldraw[fill=white,draw=black] (-2,-3) rectangle (5,1);
\draw[gray!50,dashed] (-1.9,-2.9) grid (4.9,0.9);
\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 (.05,-1) -- (-.05,-1) node[left] {$-1$};
\draw (1,0.05) -- (1,-0.05) node[outer ysep=3mm,below] {$1$};
\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}};
\drawshadow{tab}{black}
\end{tikzpicture}
\end{center}

\begin{itemize}
\item $\color{green!50!black}\mathcal{T}$ est la tangente à $\mathcal{C}_f$ au point d'abscisse 0.
\item $\color{red}{\cal T}_1$ est la tangente à ${\cal C}_g$ 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, répondez aux questions suivantes.

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

