4. (a) Let f be a function which is three-times differentiable on [c1, c2]. If at the end-points of the interval we have f(c) = f'(c) = f(c) = f'(c) = 0, prove that there exists dE (C1, C2) such that f"" (d) = 0. (b) Let f be a non-negative function which is three-times differentiable on (a,b). If there exist two points C1, C2 E (a, b) such that f(c) = f(c2) = 0, prove that there exists d E (a, b) such that f"" (d) = 0, using the result from (a).