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\documentclass{article}
\usepackage{mpgraphics}
\begin{document}
\begin{mpdisplay}
LaTeX_unitlength := 1.0pt;
w := 60*LaTeX_unitlength;
h := 40*LaTeX_unitlength;
numeric xmin, xmax, ymin, ymax;
xmin := 1/4; xmax := 6; ymax := 1/xmin; u := 1cm;
vardef f(expr x) = 1/x enddef;
xinc := 0.1;
path pts_f;
pts_f := (xmin,f(xmin))*u
for x=xmin+xinc step xinc until xmax:
.. (x,f(x))*u
endfor;
path hline[], vline[];
hline0 = (0,0)*u -- (xmax,0)*u;
vline0 = (0,0)*u -- (0,ymax)*u;
vline0.5 = (0.5,0)*u -- (0.5,ymax)*u;
vline4 = (4,0)*u -- (4,ymax)*u;
fill buildcycle(hline0, vline0.5, pts_f, vline4)
withcolor 0.8[blue,white];
draw hline0; draw vline0; % draw axes
draw (0.5,0)*u -- vline0.5 intersectionpoint pts_f;
draw (4,0)*u -- vline4 intersectionpoint pts_f;
draw pts_f withpen pencircle scaled 2;
label.bot(btex $x$ etex, (0.9xmax,0)*u);
label.lft(btex $y$ etex, (0,0.9ymax)*u);
label.urt(btex Hello $f(x)$ etex, (0.5,f(0.5))*u);
\end{mpdisplay}
\end{document}
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