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Convex and concave functions

10/05/2011

For details see wiki for convex functions and concave functions. Here I want to highlight something. How to  judge the convexity of  a function?

1. Using most basic definition of convex functions. what is the most basic definition of convex function?

2. Using definition of midpoint convex. For me, functions usually are smooth (with arbitrary order derivative).

3. See whether the first order derivative monotonically non-decreasing.

4. See whether the second order derivative is non-negative.

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