Ich würde da jetzt nicht direkt auf
pgfplots setzen. Das reine
pgf/tikZ kann auch ganz gut rechnen.
\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage{tikz}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[
declare function={f(\x)=-\x^3+\x;},
scale=10,
>=stealth
]
\draw[<->] (0,0.5) node[above left] {$P$} |- (1.25,0) node[below right] {$V$};
\draw[domain=0:1,samples=50] plot (\x,{f(\x)});
\foreach \x in {0.3,0.577,0.8}
\draw[-*,dashed,shorten >=-2pt] (\x,0) -- (\x,{f(\x)});
\draw (0.3,{f(0.3)}) node[above left] {$\dfrac{dP}{dV}>0$};
\draw (0.577,{f(0.577)}) node[above] {$\dfrac{dP}{dV}=0$};
\draw (0.8,{f(0.8)}) node[above right] {$\dfrac{dP}{dV}<0$};
\draw[->] (0.2,-0.025) -- (0.4,-0.025) node[midway,below] {Increase $V_\text{out}$};
\draw[<-] (0.7,-0.025) -- (0.9,-0.025) node[midway,below] {Decrease $V_\text{out}$};
\draw (0.577,{f(0.577)}) node[above=2.5em] {Optimum $V_\text{out}$};
\end{tikzpicture}
\end{document}
Thorsten