\subsection{Maximum et minimum d'une fonction}

\begin{definition}[Intuitive]
Sur un intervalle $I$,
\begin{itemize}\item  le \textbf{maximum} d'une fonction $f$ est la
plus grande des valeurs prises par
$f(x)$;
\item le \textbf{minimum} d'une fonction $f$ est la plus petite des
valeurs prises par
$f(x)$.
\end{itemize}
\vspace{1.5em}

\parbox{0.49\linewidth}{
Maximum en $x_0$

\begin{tikzpicture}[general, yscale=0.6]
\axeX{-1.25}{4.76}{-1,1,2,3,4}
\axeY{-1.22}{4.24}{-1,1,2,3}
\origine
\draw[tres epais, color=A1, smooth,samples=100,domain=1.0:4.0]
plot(\x,{0-((\x)-2.5)^2+3.5});
\draw [dotted, color=B1prime] (0,3.5)-- (2.49,3.5);
\draw [dotted, color=B1prime] (2.49,3.5)-- (2.49,0);
\draw  [color=B1prime] (2.49,3.5)node{$\bullet$};
\draw  [color=B1prime] (0,3.5)node{$\bullet$};
\draw[color=B1prime] (0,3.5) node[left] {{\boldmath$M$}};
\draw  [color=B1prime] (2.49,0)node{$\bullet$};
\draw[color=B1prime] (2.5,0) node[below] {{\boldmath$x_0$}};
\end{tikzpicture}
}\hfill\parbox{0.49\linewidth}{
Minimum en $x_0$

\begin{tikzpicture}[general, yscale=0.6]
\axeX{-1.23}{4.57}{-1,1,2,34}
\axeY{-1.23}{4.23}{-1,1,2,3}
\origine
\draw[tres epais, color=A1, smooth,samples=100,domain=1.0:4.0]
plot(\x,{0+((\x)-2.5)^2+0.5});
\draw [dotted, color=B1prime] (0,0.5)-- (2.49,0.5);
\draw [dotted, color=B1prime] (2.49,0.5)-- (2.49,0);
\draw  [color=B1prime] (2.49,0.5)node{$\bullet$};
\draw  [color=B1prime] (0,0.5)node{$\bullet$};
\draw[color=B1prime] (0,0.5) node[left] {{\boldmath$m$}};
\draw  [color=B1prime] (2.49,0)node{$\bullet$};
\draw[color=B1prime] (2.5,0) node[below] {{\boldmath$x_0$}};
\end{tikzpicture}
}
\end{definition}
