I am trying to prove that the global maxima of the following function $f_n(x_1,\ldots,x_n):=\exp(-\sum_{i=1}^n x_i ^2)\prod_{1\leq i
I expect this to be true, but I have no proof. I have checked it numerically for $n=2,3,4$, and I am trying to come up with a nice proof of this fact without much success.
Any suggestions would be appreciated!