Assuming the second derivative f"(x)>0 of a convex function f(x) exists over an interval (a,b).

Is it correct saying that the extremes (min, max, relative or absolute) of f"(x) always occur at the same ordinates where the extremes* of f(x) occur?

(*) Not necessarily of the same type, min or max as in f”(x): can be opposite.

I cannot depict an example that says "NO, it's not correct".

I would appreciate either such an example or few words that help me proving the above statement is correct.