1) The cost, in thousands of dollars, of airing x television commercials during a sports event is given by:
C(x) = 150 + 2,700x − 0.06x²
(a) Find the marginal cost function C'(x).
(b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars.

a) Marginal Cost function C'(x) =  2700 - 0.12x

(b) Marginal cost to approximate 5th commercial C'(4) = $2,699,520

Explanation:

The cost, in thousands of dollars, of airing x television commercials during a sports event is given by:  C(x) = 150 + 2,700x − 0.06x²

a) Marginal Cost function is = C'(x)

   C'(x) = d/dx (150 + 2,700x − 0.06x²)

   C'(x) = 0 + 2,700 − 0.06(2x)

   C'(x) = 2700 - 0.12x

(b) Marginal cost to approximate 5th commercial is C'(4).

   C'(4) = 2700 - 0.12(4)

   C'(4) = 2700 - 0.48

   C'(4) = 2699.52

  In dollars, C'(4) = $2699.52 x 1000

                            = $2,699,520

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