Second derivative test

'Second derivative test:

 classify the critical points based on the sign of f(a).

   Note that it is possible that a is a minimum and f′′(a) = 0. Example: y = x4 at a = 0.

Recall also

First derivative test: classify the critical points based on change of the sign of f'(a)

   f′(x) > 0 for x < a and f′(x) < 0 for x > a,
   f′(x) < 0 for x < a and f′(x) > 0 for x > a,
   no change.