Question

General question about Absolute Max/Min:

My book suggests to find them, we find critical points of the function, evaluate the function at each critical point and at the endpoints. Then, the absolute max (min) is the largest (smallest) of these.

Answer 1

This makes sense unless we obtain something like inflection points as our critical points. How can this method guarantee that the largest value we find is actually a max, and not an inflection point? (Or is this because it can't happen because the concativity of the function can't allow this?)

I'm trying to think of counterexamples but it's getting late where I am :(