T/F: If f has local extrema at x = c then f'(c) = 0 must hold?

Question

My answer: T, assuming f'(c) exists. At the extreme point in f the slope is equal to 0, leaving the slop of the tangent line (f'(c)) = 0.

Correct?

Answer 1

true
if there's a local extrema, then f curves down in each direction and the slope there is 0