What Are Critical Points? - Expii

A stationary point of a function f(x) is a point x=a where the derivative f'(a) exists and is zero (i.e. f'(a) = 0). The phrase critical point is a little more ambiguous: some people say it's synonymous to stationary point (derivative exists and vanishes), while others say a critical point is a point where the derivative either doesn't exist, or exists and vanishes. Either way, the concept is more important than the vocabulary.