Does the function satisfy the hypotheses of the mean value theorem on the given interval? Give reasons for your answer. f(x)=x (1-x) [0,1] Choose the correct answer. OA. No, f(x) is differentiable at every point in (0,1) but is not continuous at every point in [0,1]. OB. Yes, f(x) is continuous at every point in [0,1] and differentiable at every point in (0,1). OC. No, f(x) is continuous at every point in [0,1] but is not differentiable at every point in (0,1). OD. Yes, f(x) is continuous at every point in (0,1) and differentiable at every point in [0,1].