Question

A critical point of a function is it's extremum

Answer 1

Answer:

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Step-by-step explanation:

If c is a critical point for f(x), such that f '(x) changes its sign as x crosses from the left to the right of c, then c is a local extremum.

Answer 2

Answer:

Every local extremum in the interior of the domain of a differentiable function is neccesarily a critical point, i.e. f′(x)=0 is a necessary condition for x to be a local extremum. There are critical points which are not local extrema.