The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function.

Question

C(x) = 2000 + 2x − 0.0001x^2 (0 ≤ x ≤ 6000)
(a) What is the actual cost incurred in producing the 951st and the 2181st disc? (Round your answers to the nearest cent.)
(b) What is the marginal cost when x = 950 and 2180? (Round your answers to the nearest cent.)

Answer 1

(a) do you mean average cost, not actual cost? If so, then for the 951st disc that is just
C(951)/951 = $4.01

(b) dC/dx = 2 + 0.0002x
so for the 951st disc, that would be $2.19

Answer 2

Hmmm. For the actual cost of the nth disc, that would be
C(n) - C(n-1)
so for the 951st disc, that is
C(951)-C(950) = 3811.56 - 3809.75 = $1.81