Please answer all questions

You must show all your work to receive full credit. 1. 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) (1 point) Find the marginal cost function C'(x). b) (1 point) Use the marginal cost function to estimate how fast the cost (in thousands of dollars) is increasing at x = 4. The cost is going up at the rate of $ per tv commercial. c) (1 point) Compare this with the exact cost (in dollars) of airing the fifth commercial. The exact cost of airing the fifth commercial is $ d) (2 points) Find the average cost function C(x) and then evaluate C(4) in thousands of dollars. 2. The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula C(x) = 100 + 36x - 0.07x2 a) (1 point) Find the marginal cost function C'(x). b) (1 point) Use the marginal cost function to determine how fast the cost is going up (in $) at a production level of x = 100 teddy bears. The cost is increasing at a rate of per teddy bear. c) (1 point) Compare this with the exact cost of producing the 101st teddy bear (in $). The exact cost of producing the 101st teddy bear is d) (2 points) Find the average cost function C(x) and evaluate C(100)