I am a bit confused with the following:
We know if a function is convex then critical points are global minima. Is the converse also true? That is if we know that the set of the critical points are infact the global minima, will it imply that the function is convex?
I am not being able to come up with a counter example in 1 dimension. Nor can I prove it in general. Any help is appreciated.
I mean I guess one can ask what happens if there are no critical points for example say $|x|$ but I guess even in general this is a nice question which sort of asks about even the most basic of concepts