I have a question for Q4 in the exam 2020. How to prove that function D is strictly convex? I can prove it is convex but I am confused with the fact that it is also strictly convex. Thank you.
you can check the definition, which is almost the same thing except with > instead of >=
Thank you for your reply.
If we consider to check by calculating the second-order derivative of the function, we can see that it is not strictly larger than 0 for all x ( f''(0) = 0). Does it mean that it is not strictly convex? Or to prove the convexity, we should always check the definition but not the second-order derivative. Thank you.