An automobile dealer can sell 12 cars per day at a price of $16,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $13,000, and fixed costs are $1000, what price should he charge to maximize his profit? How many cars will he sell at this price?

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.