An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function p(x) = x3 – 4x2 + 3x – 12, where p is in hundreds of dollars and x is the number of years elapsed after the company starts operations. in how many years (x) will the company break even (no profit, no loss)? 1 year

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.