Hilfe beim Erstellen von Kennlinienfeldern und Markieren von Flächen zwischen den Kurven.

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[
    hilfslinie/.style = {help lines, dashed},
    funktion/.style = {black, thick, mark = none}
  ]
  \begin{axis}[
      axis y line = left,
      axis x line = bottom,
      xtick       = \empty,
      ytick       = \empty,
      samples     = 160,
      domain      = 0:5,
      xmax = 6,
      ymax = 6,
    ]
    \addplot[funktion, name path global = funktion1] {sqrt(x)};
    \addplot[funktion, name path global = funktion2] {2*sqrt(x)};
    \addplot[gray!60] fill between [
      of = funktion1 and funktion2,
      soft clip = {domain = 0:3}
    ] ;
    \path[name path = linie] (axis cs:3,0) -- (axis cs:3,4);
    \draw[hilfslinie, name intersections = {of = funktion1 and linie}]
      ({axis cs:3,0}-|intersection-1) -- (intersection-1);
    \draw[hilfslinie, name intersections = {of = funktion1 and linie}]
      ({axis cs:0,0}|-intersection-1) -- (intersection-1);
    \draw[hilfslinie, name intersections = {of = funktion2 and linie}]
      ({axis cs:0,0}|-intersection-1) -- (intersection-1);
  \end{axis}
\end{tikzpicture}
\end{document}