(5) Let 2 := {(r, y) E R | 1 < r + y < 4}...

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(5) Let 2 := {(r, y) E R² | 1 < r² + y < 4} be a punctured disc and let f: 0R be a continuous function which is "locally convex" (that is for every point r in the interior of N there is a small open ball on which f is convex). Suppose that the maximum of f on 2 occurs at an interior point ro of 2. Prove that f must be a constant function on 2. (5) Let 2 := {(r, y) E R² | 1 < r² + y < 4} be a punctured disc and let f: 0R be a continuous function which is "locally convex" (that is for every point r in the interior of N there is a small open ball on which f is convex). Suppose that the maximum of f on 2 occurs at an interior point ro of 2. Prove that f must be a constant function on 2.

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on 2 But as f is ilocally converx we must have uo ... View the full answer