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

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

\begin{document}

\begin{tikzpicture}[x=0.82cm,y=0.82cm,xmin=0,xmax=16,xgrille=1,xgrilles=0.5,ymin=-2,ymax=6,ygrille=1,ygrilles=0.5]
	\GrilleTikz \AxesTikz[ElargirOx=0/0,ElargirOy=0/0]
	\AxexTikz{0,1,...,15} \AxeyTikz{-1,0,...,5}
	\draw (16,0) node[above left,font=\small] {$x$} ;
	\draw (0,6) node[left,font=\small] {$y$} ;
	\clip (\xmin,\ymin) rectangle (\xmax,\ymax) ;
	\draw[very thick,blue,domain=0.01:16,samples=500] plot (\x,{3*\x-\x*ln(\x)-2*ln(\x)}) ;
	\draw (10.5,2) node[blue,above right,font=\large] {$\mathcal{C}_f$} ;
\end{tikzpicture}

\end{document}