You want to open a bakery that sells just pies and cakes. You can make a profit of $12 on each pie and $13 on each cake. It takes 2 hours to prepare one pie and 1 hour to prepare one cake. It takes 2 hours for a pie to bake and cool. It takes 2.5 hours for a cake to bake and cool. The maximum preparation time available iis 14 hours. The maximum bake time available is 18 hours. How many of each should be made to maximize profits?

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.