图形，添加对应点并在轴中心添加 0

Question

我有这个代码来实现这个功能

\documentclass{article}
\usepackage{pgfplots}

\def\FunctionF(#1){(#1)^3- 3*(#1)}%

\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis y line=center,
        axis x line=middle, 
        axis on top=true,
        xmin=-5.5,
        xmax=5.5,
        ymin=-45,
        ymax=45,
        height=12.0cm,
        width=12.0cm,
        grid,
        xtick={-5,...,5},
        ytick={-40,-32,...,40},
    ]
    \addplot [domain=-5:5, samples=50, mark=none, ultra thick, blue] {\FunctionF(x)};
    \node [left, blue] at (axis cs: 3.6,42) {$x^3-3x$};
\end{axis}
\end{tikzpicture}
\end{document}

但我需要添加这个，就像你看到的红色一样

如何添加对应点，如果可以用不同的颜色更好

并且，在轴交叉点的中心添加零，因为水平方向从 -1 跳到 1，垂直方向从 -8 跳到 8。

谢谢

Answer 1

像这样？

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
declare function = {f(\t)=(\t)^3- 3*(\t);},
        height=12.0cm,
        width=12.0cm,
        axis lines=center,
        grid,
        xmin=-5.5,
        xmax=5.5,
        ymin=-45,
        ymax=45,
        ticklabel style = {font=\footnotesize,  inner sep=1pt,
                           fill=white},
        xtick={-5,...,2,4,5},
        ytick={-40,-32,...,40},
        extra x ticks = {0,3},
        extra y ticks = {18},
        extra x tick style = {grid=none, color=red},
        extra y tick style = {color=red}
    ]
\addplot +[domain=-5:5, samples=51, mark=none, ultra thick] {f(x)} 
    node [pos=0.7, left=2mm] {$x^3-3x$};
\draw[dashed, semithick, red]  (3,0) |- (0,18) node[pos=0.5, circle, inner sep=2pt, fill=red] {};
\end{axis}
\end{tikzpicture}
\end{document}