At which point does $f(x) = 2 x^{3} + 3 x^{2} - 12 x + 1$ have a local maximum?

Explanation

1. 01

   $f'(x) = 6 \left(x - 1\right) \left(x + 2\right)$.

2. 02

   $f'$ changes from positive to negative at $x = -2$, so $f$ rises then falls there: a local maximum.