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

That's the answer above