Question: 3. Let f(r) be a continuous function and define F(x) = f (t) dt (a) If possible, find a number c E R such that

3. Let f(r) be a continuous function and define F(x) = f (t) dt (a) If possible, find a number c E R such that F(c) = 0. If not possible, explain why not. (b) Alice claims the average value of f(x) on [0, 2] is - F(1). Is she correct? Explain your answer. (c) For this part only, suppose f(x) = In(x2 + 1). What is F'(x)? Show your work

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