%% Autor: X. Rendtel 
%% Letzte Aenderung: 03.10.2009 

\documentclass[10pt, a4paper]{article} 
\usepackage[utf8]{inputenc}
\usepackage{pstricks,pst-pdf,pst-node,xcolor,pst-circ,pst-func,pst-math,pst-eucl,pstricks-add}
\usepackage{amsmath,amssymb,amscd,ziffer}
\makeatletter\newcommand{\psxpoint}[3][black]{%
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  \rput[t](! #2 \pst@number\pslabelsep \pst@number\pst@xticksizeB add
  \pst@number\psyunit div neg ){\color{#1}#3}} \makeatother
\makeatletter\newcommand{\psypoint}[3][black]{%
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\makeatother
\pagestyle{empty} 

\begin{document}
\psset{linecolor=black, fillcolor=black!20, linewidth=1pt, 
  dotstyle=*, plotpoints=1000, dotsize=3pt, arrowsize=3pt 2, 
  arrowinset=0.25, xunit=1cm, yunit=1cm} 

\begin{pspicture}(-10,-10)(10,10)
  
  %% Einschluss zwischen den Funktionen ((0.5*x^2)+1) und (-(x^2))+((3/2)*x)+4 
  \pscustom[fillcolor=red!40]{\gsave% 
    \psplot[linestyle=solid, linewidth=0.2pt]{-1}{2}{0.5 x  dup  mul  mul  1  add  }% 
    \psplot[linestyle=solid, linewidth=0.2pt]{2}{-1}{x dup  mul  neg  3  2  div  x  mul  add  4  add  }% 
    \fill[fillstyle=solid, fillcolor=red!40]\grestore}% 
  
  \uput{0}[180]{0}(4,-0.7){$x$}% 
  \uput{0}[0]{0}(0.2,4.8){$y$}% 
  \psaxes[linestyle=solid, linewidth=0.8pt, showorigin=false,comma, 
  subticks=0, Dx=1, Dy=1, dx=0pt, dy=0pt, Ox=0, Oy=0]{->}(0,0)(-3,-1)(4,5)% 
  
  \rput[bl](2.6,1.5){$g(x) = -x^2+\frac{3x}{2}+4$} 
  \rput[bl](2.8,3.3){$f(x) = \frac{1}{2}x^2+1$} 
  
  \psplot[linestyle=solid, algebraic]{-2.8248}{2.8228}{0.5*x^2+1}% 
  \psplot[linestyle=solid, algebraic]{-1.6056}{3.1031}{-x^2+(3/2)*x+4}% 
  \psline[linestyle=dashed](2,3)(2,0)% 
  \psxpoint{2}{} 
  \psline[linestyle=dashed](2,3)(0,3)% 
  \psypoint[black]{3}{} 
  \psdot[linestyle=dashed, dotstyle=x, dotsize=1pt](2,3)% 
  
\end{pspicture} 
\end{document} 
