Consider the following function $$ f(x,y)=\log\left(1 - \frac{x}{1+y} -\frac{y}{1+x} \right) $$ defined on $0\leq x\leq1$ and $0\leq y\leq1$. The plot of this function looks quite concave but I would like a proof. Ideally without using the Hessian directly so I can generalize the argument easily. Any suggestions would be greatly appreciated!
2026-05-05 04:02:42.1777953762
Concavity of the log of a simple equation
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