3. Prove the following theorem: Theorem 2. Assume a > 0. Let f be continuous on...

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3. Prove the following theorem: Theorem 2. Assume a > 0. Let f be continuous on [0, a]. Suppose for any 02Sa, we have fof(t)dt = f(x). Then there exists c ER such that f(x) = cx on [0, a]. Hint: Let h(x): f(x) What is the derivative of h(x) if f is differentiable on (0, a)? X 3. Prove the following theorem: Theorem 2. Assume a > 0. Let f be continuous on [0, a]. Suppose for any 02Sa, we have fof(t)dt = f(x). Then there exists c ER such that f(x) = cx on [0, a]. Hint: Let h(x): f(x) What is the derivative of h(x) if f is differentiable on (0, a)? X