David throws a bucket with an initial speed of 2 meters per second into a well that is 30 meters deep. When will the bucket hit the bottom of the well? A. About 2.69 seconds
B. About 30 seconds
C. About 3.82 seconds
D. About 4.21 seconds

A

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.