A student has 6 engineering books, 3 math books, and 2 statistics books. She wants to put them on three shelves (top, middle, bottom) with each shelf containing only books of a single discipline, but the order on each shelf is completely free. In how many total ways can she do this ?

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.