Calculating plot intersections

In Chapter 10, Calculating with Coordinates and Paths, we calculated the intersection points of TikZ paths. Similarly, we can let pgfplots determine the intersections of plots. If you use the fillbetween library as we did in the previous section, pgfplots will automatically load the TikZ intersections library. Otherwise, you can load it yourself.

First, we need to give each plot path a name. Then, we can calculate the intersection points as we did in Chapter 10, highlighted here:

\begin{axis}[axis lines = center, axis equal,
    domain = -1.5:1]
  \addplot[name path=cubic]   {x^3/5 - x};
  \addplot[name path=quartic] {(x^2-1)^2};
  \fill[name intersections = {of=cubic and quartic,
   name=p}]
    (p-1) circle (2pt) node [above right] {$p_1$}
    (p-2) circle (2pt) node [left]        {$p_2...