Does the function satisfy the hypotheses of the mean value theorem on the given interval? Give reasons for your answer. f(x) = 1x (3 - x) ; [0, 3] Choose the correct answer. O A. No, f(x) is continuous at every point in [0,3] but is not differentiable at every point in (0,3). O B. Yes, f(x) is continuous at every point in (0,3) and differentiable at every point in [0,3]. O C. No, f(x) is differentiable at every point in (0,3) but is not continuous at every point in [0,3]. O D. Yes, f(x) is continuous at every point in [0,3] and differentiable at every point in (0, 3)