Question

What is difference between critical points and inflection points?

Answer 1

In the textbook I use (Stewart Calculus)

critical point of `f` = critical number for `f` = value of `x` (the independent variable) that is 1) in the domain of `f`, where `f'` is either `0` or does not exists. (Values of `x` that meet the conditions of Fermat's Theorem.)

An inflection point for `f` is a point on the graph (has both `x` and `y` coordinates) at which the concavity changes.

(Other people seem to use other terminology. I don't know f they ate mistaken or just have different terminology.. But the textbooks I've used in the U.S since the early 80s have all used this definition.)