What types of points are critical points?

2 Answers
Steve M
Oct 12, 2016

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.

Jim H
Oct 12, 2016

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.

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