Derivative Test

First Derivative Test §

First derivative test is when f’ changes from negative to positive at x = a or positive to negative (has a minimum or maximum)

If f has a local minimum at x=a on domain ,   0 or undefined, and f’changes from negative to positive.

Second Derivative Test §

If f’(a) = 0 and f”(a) > 0 then f has a Minimum

If f’(a) = 0 and f”(a) < 0 then f has a Maximum

If f has a local minimum at x=a on the domain 0 and > 0.