Is a critical number basically a function's vertex?

Question

Calc I, no need to get extreemly complicated

How does (0,0) fit the definition of a critical point on x^3?

Answer 1

You're very much on the right track.

A critical point that's a maximum or minimum is a whole lot like a vertex.

A critical point that's an inflection point, however -- not so much.

For example, the origin is a critical point of y = x^3, and that's not really a lot like a vertex.