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\documentclass[margin=5mm]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{xcolor}
\usepackage{tikz}
\usepackage{pgffor}

\begin{document}

\begin{tikzpicture}%[-5:0.1, samples=500]

\coordinate[label=right:X] (X) at (5.5,0);
\coordinate[label=right:Y] (Y) at (0,2);
\draw[step=0.5cm,gray,very thin] (-1.4,-4.4) grid (5.9, 2.4);
%\draw[->, line width=1pt, red] (0,0) -- (3,1);
%\draw[-, line width=1pt, blue] (0,0) -- (1,4) -- (2,4);
\draw[<->, line width=1pt, black] (X) -- (0,0) -- (Y);
\draw[-, line width=1pt, black] (-1,0) -- (0,0) -- (0,-4);
\foreach \i in {1,-1,-2,...,-3}{
\draw[line width=1pt] (-0.2, \i) -- (0, \i);
\coordinate[label=left:\i] (\i) at (-0.2,\i);
}
\foreach \i in {5,...,1}{
\draw[line width=1pt] (\i, -0.2) -- (\i, 0);
\coordinate[label=\i] (\i) at (\i,-0.7);
}
% 0 zufügen, Position evtl. anpassen
\coordinate[label=0] (0) at (0.12,-0.7);
\draw [line width=1.3pt,smooth,color=black!65!green,samples=100,domain=-0.5:5] plot({\x},{4*\x*e^(-\x)});
\node [color=black!65!green] at (1.6,1.64) {f};
% Titel zufügen
\node[align=center,yshift=1em] 
    at (current bounding box.north)
    {Hier ist ein Titel};
% copyright zufügen		
\node[align=center,yshift=-1em] 
    at (current bounding box.south)
    {copyright?};		
\end{tikzpicture}

\end{document}