A bag contains 3 red marbles, 7 blue marbles, and 4 green marbles. If a green marble is drawn you win $2, and if a red marble is drawn you win $1. Drawing a blue marble causes you to lose $1. Suppose you make 64 draws out of the bag Your chances remain the same, the number of red, blue and green marbles doesn't change from draw to draw. This corresponds to drawing how many tickets at random

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.