4. Let f be a function continuous on [0, 1] and twice differentiable on (0,1). (a) Suppose that = 0 and f(c) > 0 for some c € (0, 1). f(0) = f(1) = 0 and Prove that there exists xo € (0, 1) such that f"(ro) < 0. (b) Suppose that f* f(x) dx = f(0) = f(1) = 0. Prove that there exists a number xo € (0, 1) such that f"(xo) = 0.

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