Problem 1248 (difficulty: 5/10)

Assume that \(\displaystyle f:\R^2\to\R\) has a second partial derivative \(\displaystyle D_{12}f\) and for all \(\displaystyle a<b\), \(\displaystyle c<d\) we have \(\displaystyle f(a,c)+f(b,d)\ge f(a,d)+f(b,c)\). Show that \(\displaystyle D_{12}\) is non-negative.

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