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

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

\begin{document}

\begin{tikzpicture}[x=1.25cm,y=1.25cm,xmin=-6,xmax=6,xgrille=1,xgrilles=0.2,ymin=-1,ymax=5,ygrille=1,ygrilles=0.2]
	\def\tmpvalalpha{3.92153}
	\GrilleTikz[][thin,lightgray][ultra thin,lightgray] \AxesTikz[ElargirOx=0/0,ElargirOy=0/0]
	%\AxexTikz{} \AxeyTikz{grady}
	\clip (\xmin,\ymin) rectangle (\xmax,\ymax) ;
	\draw (0,0) node[below left=2pt] {$O$} ;
	\draw[line width=1pt,->,>=latex] (0,0)--++(1,0) node[midway,below] {$\vv{\imath}$} ;
	\draw[line width=1pt,->,>=latex] (0,0)--++(0,1) node[midway,left] {$\vv{\jmath}$} ;
	\draw[blue,line width=1.15pt,samples=2,domain=\xmin:\xmax] plot ({\x},{-0.25*\x+ln(2)}) ;
	\draw[line width=1.15pt,densely dashed] ({-\tmpvalalpha},{-0.25*(-\tmpvalalpha)+ln(2)}) -- ({-\tmpvalalpha},0) node[below] {$-\alpha$} ;
	\draw[teal,line width=1.15pt,fill=teal!10,fill opacity=0.5] ({-\tmpvalalpha},{-0.25*(-\tmpvalalpha)+ln(2)}) -- ({-\tmpvalalpha},{ln(1+exp(--\tmpvalalpha))+0.25*(-\tmpvalalpha)}) -- ({\tmpvalalpha},{ln(1+exp(-\tmpvalalpha))+0.25*(\tmpvalalpha)}) -- ({\tmpvalalpha},{-0.25*(\tmpvalalpha)+ln(2)}) -- cycle ;
	\draw[red,line width=1.15pt,samples=500,domain=\xmin:\xmax] plot ({\x},{ln(1+exp(-\x))+0.25*\x}) ;
	%labels
	\draw ({-\tmpvalalpha},{-0.25*(-\tmpvalalpha)+ln(2)}) node[below left] {$P$} ;
	\draw ({-\tmpvalalpha},{ln(1+exp(--\tmpvalalpha))+0.25*(-\tmpvalalpha)}) node[above right] {$N$} ;
	\draw ({\tmpvalalpha},{ln(1+exp(-\tmpvalalpha))+0.25*(\tmpvalalpha)}) node[above] {$M$} ;
	\draw ({\tmpvalalpha},{-0.25*(\tmpvalalpha)+ln(2)}) node[below] {$Q$} ;
	\draw ({\tmpvalalpha},{0}) node[below right] {$\alpha$} ;3
	\draw[red] (-5,3.85) node[below left,font=\large] {$\mathcal{C}_f$} ;
	\draw[blue] (-5,1.95) node[below left,font=\large] {$\Delta$} ;
\end{tikzpicture}

\end{document}