Erik just found an old set of reference books his grandfather gave him years ago. There are 12 same-sized books in the set, each being 6 inches long and 3
4
of an inch wide. The books are packed in a case shaped like a rectangular prism that fits them perfectly. The case has a volume of 432 cubic inches.
How tall are the books?

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.