Add Up Only the Peaks

A fifth-degree function is given by

$f(x) = 3x^5 - 25x^3 + 60x + 7$

It has four critical points. Some of them are local maxima and some are local minima.

Task:

1. Find all four critical points.
2. Classify each one using the second derivative test.
3. Report the sum of the function values $f(x)$ at the local maxima only.

Give an exact integer.

Do not shortcut this by picking the two largest values of $f$. On this curve the sign of $f''$ — not the size of the number — decides which points are peaks.