Problem 1247 (difficulty: 6/10)

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

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