Question: Let f : R^n R be a convex, differentiable function. Assume that there exist x, y R^n such that f(x) = f(y) = 0. Show

Let f : R^n R be a convex, differentiable function. Assume that there exist x, y R^n such that f(x) = f(y) = 0. Show that f((x + y)/2) = 0.

hint: show (x+y)/2 is a global minimizer.

Thank you!

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