TITLE: If f''(x) > 0 does it mean it can possess at most 1 point of minimum?
QUESTION [7 upvotes]: Graphically I can observe that if $f''(x)>0$ for all $x$ then it can have at most $1$ point of minimum. Is it true? If yes how can I prove it? Thank you!

REPLY [3 votes]: Comment
Is it possible to explain MVT/Rolle's thm with reference to graph?