An analyst has found that a company’s costs and revenues in dollars for one product are given by C(x) = 2x and R(x) = 6x - x²/1000, respectively, where x is the number of items produced.
(a) Find the marginal cost function.
(b) Find the marginal revenue function.
(c) Using the fact that profit is the difference between revenue and costs, find the marginal profit function.
(d) What value of x makes marginal profit equal 0?
(e) Find the profit when the marginal profit is 0.