% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage{ProfLycee}

\begin{document}

\begin{tikzpicture}[x=0.5cm,y=0.5cm,xmin=-1,xmax=14,xgrille=1,xgrilles=0.2,ymin=-3,ymax=6,ygrille=1,ygrilles=0.2]
	\GrilleTikz[][very thin,gray][very thin,lightgray]
	\AxesTikz[Epaisseur=0.75pt,ElargirOx=0/0,ElargirOy=0/0]
	\OrigineTikz[Police=\tiny,Decal=0pt]
	\AxexTikz[Epaisseur=0.75pt,AffOrigine=false,Police=\tiny,HautGrad=3pt]{-1,0,...,13}
	\AxeyTikz[Epaisseur=0.75pt,AffOrigine=false,Police=\tiny,HautGrad=3pt]{-3,-2,...,5}
	\FenetreTikz
	\CourbeTikz[thick,red,samples=500]{10*(\x-1)*exp(-0.5*\x)}{0:14}
	\draw[<->,>=latex,CouleurVertForet,thick] ({2.25},{(10*3-10)*exp(-0.5*3)}) -- ({3.75},{(10*3-10)*exp(-0.5*3)}) ;
	\draw[red] (10,1.25) node[below right=0pt,font=\scriptsize] {$y=f(x)$} ;
	\CourbeTikz[thick,densely dashed,blue,samples=2]{-10*exp(-2.5)*(\x-5)+40*exp(-2.5)}{0:14}
	\filldraw (5,{(10*5-10)*exp(-0.5*5)}) circle[radius=1.5pt] node[above right,font=\scriptsize] {$P$} ;
\end{tikzpicture}

\end{document}