The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 5,000x + 0.05x^2.
(a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 4 thousand dollars. Compare this with the exact cost of airing the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ . Thus, there is a difference of $ .
(b) Find the average cost function C, and evaluate C(4). What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.