Consider a firm that is facing the following demand function for it's output

x: P(x) = 2400 - 5x and the following total cost function: C(x) = 2x3 - 15x2 + 400x. The firm wants to maximize profit.

a. Find the firm's profit function. Show your work.

b. Find all critical points of the profit function. Show your work

c. Use calculus to evaluate the critical points to determine which one corresponds to the profit maximum output. You must also prove that the other critical point(s) is (are) not profit maximizing. Show your work.