Question: Let f Rn R be a function and let S:={(x,y)RnR|yf(x)}. Assuming S is a convex set, prove that f is a convex function. Hint: consider

Let f Rn R be a function and let S:={(x,y)RnR|yf(x)}. Assuming S is a convex set, prove that f is a convex function. Hint: consider the points (sx1 + (1 s)x2, sf(x1) + (1 s)f(x2)) Rn R.

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