\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)
	% dérivée fp=1./48.*(-6*x*x-18*x)
	\shorthandoff{:}
	\draw[-,blue,thick] plot[id=temp,smooth,domain=-2.5:3.2,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] (P1) {};%(1,2)%(-1,2.083333)
	%\draw[blue,fill=blue] (P0) circle (0.05);%
	%\draw[blue] (P1)+(.35,.2) node {$P_1$};%
	\draw[->,>=latex,thick] (0,0) -- (P1) node[left,pos=0.5] {$\vec{r}_1$};%
	% tangente
	\shorthandoff{:}
	%\draw[dashed,cyan] plot[id=temp,smooth,domain=-1.8:4,samples=2] function{-.5*(x-1)+2} node[shape=coordinate] () {};
	%\path[cyan] (-1.5,3.25) -- node[above,sloped] {tangente} +(1,-.5);%
	\pgfmathsetmacro{\valPente}{1./48.*(-6*\valX*\valX-18*\valX)};
	\draw[dashed, brown] (P1)+(-1*2.5,-\valPente*2.5) -- node[above,sloped,pos=0.2] {tangente} +(1*2.5,\valPente*2.5);%
	\shorthandon{:}
	% point 2
	\pgfmathsetmacro{\valX}{1.2};
	\pgfmathsetmacro{\valY}{1./48.*(-2*\valX*\valX*\valX-9*\valX*\valX+107)};
	\path (\valX,\valY) node[shape=coordinate] (P2) {};
	%\draw[blue,fill=blue] (P2) circle (0.05);%
	%\draw[blue] (P2)+(.2,.3) node {$P_2$};%
	\draw[->,>=latex,thick] (0,0) -- (P2) node[below right,pos=0.5] {$\vec{r}_2$};%
	% vitesse
	\draw[->,>=latex,thick,vitCol] (P1) -- +(1*1.5,\valPente*1.5) node[above,pos=0.5] {$\vec{v}$};%
	% d\'{e}placement
	\path (P1) -- (P2) node[above=3pt,pos=0.5] {$\Delta\vec{r}$};%
	% origine
	\draw[-] (0,-.1) -- (0,+.1) node[below left,pos=0.6] {$O$};%
	\draw[-] (-.1,0) -- (.1,0) node[below] {};%
\end{tikzpicture}%

\end{document}