

\begin{definition}[Maximum, minimum et  extremum d'une fonction]
    \begin{itemize}
        \item Dire que $f$ admet un \MotDefinition{maximum}{}  en $a$ sur l'intervalle $I$
            signifie que :\\
            Il existe un réel $M$ tel que pour tout  $x$ dans $I$: $f(x)\leqslant M$ et $M=f(a)$.
        \item Dire que $f$ admet un \MotDefinition{minimum}{} en $b$ sur l'intervalle $I$
            signifie que :\\
            Il existe un réel $m$ tel que pour tout $x$ dans $I$: $f(x)\geqslant m$ et $m=f(b)$
\item Un \MotDefinition{extremum}{} est le terme générique pour désigner un maximum ou un minimum.
\end{itemize}
\parbox{0.49\textwidth}{   
\begin{tikzpicture}[general]
\axeX{-1.25}{4.73}{-1,1,2,3,4}
\axeY{-0.9}{3.24}{1,2,3}
\origine
\draw[epais, smooth,samples=100,domain=1.0:4.0, color=A1]
plot(\x,{0-((\x)-2.5)^2+2.5});
\draw [dotted] (0,2.5)-- (2.49,2.5);
\draw [dotted] (2.49,2.5)-- (2.49,0);
\draw [dotted] (0,1.59)-- (1.55,1.59);
\draw [dotted] (1.55,1.59)-- (1.55,0);
\draw  [color=B1prime] (2.49,2.5)node{$\bullet$};
\draw  [color=B1prime] (0,2.5)node{$\bullet$};
\draw[color=B1prime] (0,2.5) node[left] {{\boldmath$M$}};
\draw  [color=B1prime] (2.49,0)node{$\bullet$};
\draw[color=B1prime] (2.49,0) node[below] {{\boldmath$a$}};
\draw  [color=B1prime] (1.55,1.59)node{$\bullet$};
\draw  [color=B1prime] (0,1.59)node{$\bullet$};
\draw[color=B1prime] (0,1.59) node[left] {{\boldmath$f(x)$}};
\draw  [color=B1prime] (1.55,0)node{$\bullet$};
\draw[color=B1prime] (1.55,0) node[below] {{\boldmath$x$}};
\end{tikzpicture}}\hfill\parbox{0.49\textwidth}{
\begin{tikzpicture}[general]
\axeX{-1.25}{3.73}{-1,1,2,3,4}
\axeY{-0.9}{3.24}{1,2,3}
\origine
\draw[epais, smooth,samples=100,domain=1.0:4.0, color=A1]
plot(\x,{+((\x)-2.5)^2+0.5});
\draw [dotted] (0,0.5)-- (2.49,0.5);
\draw [dotted] (2.49,0.5)-- (2.49,0);
\draw [dotted] (0,1.49)-- (1.5,1.49);
\draw [dotted] (1.5,1.49)-- (1.5,0);
\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] (2.49,0) node[below] {{\boldmath$b$}};
\draw  [color=B1prime] (1.5,1.49)node{$\bullet$};
\draw  [color=B1prime] (0,1.49)node{$\bullet$};
\draw[color=B1prime] (0,1.49) node[left] {{\boldmath$f(x)$}};
\draw  [color=B1prime] (1.5,0)node{$\bullet$};
\draw[color=B1prime] (1.6,0) node[below] {{\boldmath$x$}};
\end{tikzpicture}}
\end{definition}
