3. Prove the following theorem: Theorem 2. Assume a > 0. Let f be continuous on [0, a]. Suppose for any 0 x a, we have fo(t)dt = xf(x). Then there exists c ER such that f(x) = cx on [0, a]. Hint: Let h(x) = f(x) = X What is the derivative of h(x) if f is differentiable on (0, a)?