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