\exercice[style=A,N=2,verif]{Lectures graphiques}

Pour chacune des courbes suivantes, \'etudier la convexit\'e de la fonction correspondante sur l'intervalle o\`u la courbe est trac\'ee.

Pr\'eciser, s'il y a lieu, la position des points d'inflexion.
\begin{enumerate}
\begin{multicols}{3}
\item \begin{tikzpicture}[>=stealth',baseline=4.5cm]
\draw[gray,dashed] (-1,-2) grid (2,5);
\draw[->] (-1,0) -- (2,0);
\draw[->] (0,-2) -- (0,5);
\draw[thick,violet] plot[domain=-1:2,samples=100] (\x,{\x*\x-3*\x+1});
\end{tikzpicture}
\columnbreak
\item \begin{tikzpicture}[>=stealth',baseline=1.5cm]
\draw[gray,dashed] (0,-1) grid (2,2);
\draw[->] (0,0) -- (2,0);
\draw[->] (0,-1) -- (0,2);
\draw[thick,violet] plot[domain=0.01:2,samples=100] (\x,{\x*ln(\x)});
\end{tikzpicture}
\columnbreak
\item \begin{tikzpicture}[>=stealth',baseline=5.5cm,yscale=0.1]
\draw[gray,dashed] (-1,-30) grid[ystep=10] (2,60);
\draw[->] (-1,0) -- (2,0);
\draw[->] (0,-30) -- (0,60);
\draw[thick,violet] plot[domain=-1:2,samples=100] (\x,{25*(\x-1)*(\x-2)*exp(\x)});
\end{tikzpicture}
\end{multicols}

\begin{multicols}{2}
\item \begin{tikzpicture}[>=stealth',baseline=5.5cm]
\draw[gray,dashed] (-3,-2) grid (2,6);
\clip (-3,-2) rectangle (2,6);
\draw[->] (-3,0) -- (2,0);
\draw[->] (0,-2) -- (0,6);
\draw[thick,violet] plot[domain=-3:2,samples=100] (\x,{(\x+2)*ln(\x*\x+1)});
\end{tikzpicture}
\columnbreak
\item \begin{tikzpicture}[>=stealth',baseline=4.5cm,yscale=0.333]
\draw[gray,dashed] (-5,-15) grid[ystep=3] (2.5,15);
\clip (-5,-15) rectangle (2.5,15);
\draw[->] (-5,0) -- (2.5,0);
\draw[->] (0,-15) -- (0,15);
\draw[thick,violet] plot[domain=-5:2.5,samples=100] (\x,{(\x*\x-4)*exp(0.5*\x+1)*ln(\x*\x+1)});
\end{tikzpicture}

\end{multicols}
\end{enumerate}