Assume that the cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 4,800x + 0.07x2. (a) Find the marginal cost function. HINT [See Example 1.] C'(x)= Use it to estimate how fast the cost (in thousands of dollars) is increasing when x = 4. thousand dollars per television commercial Compare this with the exact cost (in dollars) 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) (in thousands of dollars). HINT [See Example 4.] = C(x) C(4) - thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial. The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100+ 35x - 0.06x². (a) Find the marginal cost function C'(x). C'(x) = Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears. $ per teddy bear Compare this with the exact cost of producing the 101st teddy bear (in $). The cost is increasing at a rate of $ $ per teddy bear. The exact cost of producing the 101st teddy bear is . Thus, there is a difference of $ (b) Find the average cost function C, and evaluate C(100) (in $). C(x) C(100) $ per teddy bear What does the answer tell you? The average cost of producing the first hundred teddy bears is $ per teddy bear.