Question for exam 2020 Q4


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.

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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.

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