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

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

\begin{document}

\begin{tikzpicture}[x=1.3cm,y=1.3cm,xmin=0,xmax=3,ymin=0,ymax=3]
	\GrilleTikz \AxesTikz[ElargirOx=0/0,ElargirOy=0/0] \AxexTikz{0,1,2} \AxeyTikz{0,1,2}
	\draw[samples=250,very thick,red,domain=1:1.9] plot (\x,{1+\x*\x-2*\x*\x*ln(\x)}) ;
	\draw (1,2) node[above left,red,font=\large] {$A$} ;
	\draw (1.9,0) node[above right,red,font=\large] {$B$} ;
	\draw (1.9,0.05) node[below,font=\large] {$\alpha$} ;
	\draw (1.5,1.5) node[above right,red,font=\large] {$\mathcal{C}$} ;
\end{tikzpicture}

\end{document}