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

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

\begin{document}

\begin{tikzpicture}[x=2cm,y=10cm,xmin=0,xmax=3,ymin=0,ymax=0.45]
	\draw[semithick] (-0.5,0)--(\xmax,0) ;
	\draw[semithick] (0,0)--(0,\ymax) ;
	\CourbeTikz[thick,blue,samples=250]{\x*exp(-\x)}{0:\xmax}
	\draw[blue] (2.25,0.23714) node[above] {$\mathcal{C}_f$} ;
	\draw[thick,dashed] (0.75,0) node[below] {$a$} --++ (0,{0.75*exp(-0.75)}) ;
	\draw[thick,teal] (0,{0.75^2*exp(-0.75)})--({1.75},{0.25*exp(-0.75)*1.75+0.75^2*exp(-0.75)}) node[pos=0.75,above] {$T_a$};
	\draw[thick,->,>=latex] (-0.25,0)--++(0,{0.75^2*exp(-0.75)}) node[midway,left] {$g(a)$};
	\draw[thick,densely dashed] (-0.25,{0.75^2*exp(-0.75)})--++(0.25,0) ;
	\filldraw (0.75,{0.75*exp(-0.75)}) circle[fill,radius=1.5pt] node[above] {$A$} ;
	\filldraw (0,{0.75^2*exp(-0.75)}) circle[fill,radius=1.5pt] node[above left] {$H_a$} ;
\end{tikzpicture}

\end{document}