Question

What types of points are critical points?

Answer 1

Critical points are points on the graph of `y=f(x)` where the first derivative, `f'(x)` is zero. They correspond to maximum, minimum or points of inflexion on the curve.

Answer 2

In James Stewart (and others) Calculus textbook:

Explanation:

A critical number of function `f` is a number, `c`, in the domain of `f` with `f'(c)` does not exist or `f'(c) = 0`.

"Critical point" is sometimes synonymous with "critical number" and at other times it is a point on the graph of `f`, so it looks like `(c,f(c))` where `f'(c)` either does not exist or `f'(c) = 0`.

Critical points may be the locations of relative extrema. They also may not be locations of extrema.