\documentclass[convert=true,convert={convertexe={convert},density=1200,outext=.png}]{standalone}

\input{figsDefs.tex}

\begin{document}
	
\begin{tikzpicture}%
	% trajectoire f=1./48.*(-2*x*x*x-9*x*x+107)
	% deriv\'{e}e fp=1./48.*(-6*x*x-18*x)
	\shorthandoff{:}
	\draw[-,blue,thick] plot[id=temp,smooth,domain=-1:3.2,samples=30] function{1./48.*(-2*x*x*x-9*x*x+107)} node[left=3pt] {$\Gamma$};
	\shorthandon{:}
	% point 1
	\pgfmathsetmacro{\valX}{1};
	\pgfmathsetmacro{\valY}{1./48.*(-2*\valX*\valX*\valX-9*\valX*\valX+107)};
	\path (\valX,\valY) node[shape=coordinate] (P) {};
	% tangente
	\pgfmathsetmacro{\valPenteUn}{1./48.*(-6*\valX*\valX-18*\valX)};
	% acc\'{e}l\'{e}ration tangentielle
	\path (1,\valPenteUn) node[coordinate] (aT) {};
	\draw[dashed,dirCol] (P)+($-2*(aT)$) -- node[above,sloped,pos=0.2] {tangente} +($2*(aT)$);%
	\draw[->,>=latex,accCol] (P) -- +(aT) node[above,pos=0.7] {$\vec{a}_t$};%
	% acc\'{e}l\'{e}ration normale
	\path (\valPenteUn,-1) node[coordinate] (aN) {};
	\draw[dashed,dirCol] (P)+($-1.5*(aN)$) -- node[above,sloped,pos=0.8] {normale} +($3*(aN)$);%
	\draw[->,>=latex,accCol] (P) -- +(aN) node[left=2pt,pos=0.6] {$\vec{a}_n$};%
	% acc\'{e}l\'{e}ration
	\path (aT)+(aN) node[shape=coordinate] (a) {};
	\draw[->,>=latex,thick,accCol] (P) -- +(a) node[right,pos=1] {$\vec{a}$};%
	\draw[dashed,accCol] (P)+(aT) -- ++(a);
	\draw[dashed,accCol] (P)+(aN) -- ++(a);
\end{tikzpicture}%

\end{document}