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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 969250557748--
%%--Les connaissances de base sur la dérivation--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%
%

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\label{ForcePass2}\vspace{1.5cm}

\begin{exercise}
Dans chacun des cas suivants, apr\`{e}s avoir d\'{e}termin\'{e}
\textbf{l'ensemble de d\'{e}rivation} de $f$, d\'{e}terminer $f^{\prime}(x)$
et l'\'{e}quation de la tangente $T_{a}$ au point d'abscisse $a.$%

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\begin{enumerate}
\item
\[
f(x)=2x+1\quad;\quad a=1;
\]


\item
\[
f(x)=x^{2}-x+1\quad;\quad a=1;
\]


\item
\[
f(x)=(2x+1)^{3}\quad;\quad a=0;
\]


\item
\[
f(x)=\sqrt{x}+\dfrac{1}{x}\quad;\quad a=1;
\]


\item
\[
f(x)=\dfrac{1}{2x+1}\quad;\quad a=0;
\]


\item
\[
f(x)=\sqrt{2x+1}\quad;\quad a=1;
\]


\item
\[
f(x)=x\sin x\quad;\quad a=0;
\]


\item
\[
f(x)=\cos^{2}x\quad;\quad a=\pi;
\]


\item
\[
f(x)=\cos(2x+1)\quad;\quad a=-1/2;
\]


\item
\[
f(x)=\dfrac{x^{2}+1}{x-1}\quad;\quad a=0.
\]

\end{enumerate}%

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\end{exercise}

\smallskip

\begin{exercise}
Soit $f$ la fonction d\'{e}finie sur $%
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\mathbb{R}
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$ par: $f(x)=x^{2}+4x+1.$ On appelle $\mathcal{C}_{f}$ la courbe
repr\'{e}sentative de $f$ dans un rep\`{e}re $\left(  O;\overrightarrow
{i};\overrightarrow{j}\right)  .$

\begin{enumerate}
\item D\'{e}terminer les \'{e}quations des tangentes $T_{-3}$ et $T_{1}$ \`{a}
$\mathcal{C}_{f}$ aux points d'abscisses respectives $-3$ et $1;$

\item Tracer $\mathcal{C}_{f}$, $T_{-3}$ et $T_{1};$

\item D\'{e}terminer les coordonn\'{e}es du point d'intersection $I$ de
$T_{-3}$ avec $T_{1}.$
\end{enumerate}
\end{exercise}


\end{document}