Answer:
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
