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

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

\begin{document}

\begin{tikzpicture}[x=1.8cm,y=0.9cm,xgrilles=1,ygrilles=1,xmin=0,ymin=-4,xmax=8,ymax=5]
	\FenetreSimpleTikz(ElargirOx=0/0,ElargirOy=0/0){0,1,...,7}{-4,-3,...,4}
	\draw[very thick,red] plot[smooth] coordinates {%
		\xintthecoords\xintfloatexpr
		seq((x,4/(1+exp(-3*x+12))),x=0..[0.1]..+8)
		\relax
	};
	\draw[very thick,blue] plot[smooth] coordinates {%
		\xintthecoords\xintfloatexpr
		seq( ( x , (12*exp(12-3*x))/(1+exp(12-3*x))**2 ),x=0..[0.1]..+8)
		\relax
	};
	\draw[very thick,CouleurVertForet] plot[smooth] coordinates {%
		\xintthecoords\xintfloatexpr
		seq( ( x , -(36*(exp(12+6*x)-exp(24+3*x)))/(exp(12) + exp(3*x))**3 ),x=0..[0.1]..+8)
		\relax
	};
	\draw[CouleurVertForet] (4.35,-1.75) node[font=\Large] {$\mathcal{C}_1$} ;
	\draw[blue] (4.75,1.65) node[font=\Large] {$\mathcal{C}_3$} ;
	\draw[red] (4.75,4.15) node[font=\Large] {$\mathcal{C}_2$} ;
\end{tikzpicture}

\end{document}