Question

The cost, in dollars, of producing x yards of a certain fabric is

C(x) = 1500 + 15x − 0.1x² + 0.0005x³.

(a) Find the marginal cost function.
C'(x) = __?__________

(b) Find

C'(300)

and explain its meaning. What does it predict?

C'(300) = ____?______

and this is the rate at which costs are increasing with respect to the production level when

x = ___?______ .

C'(300) predicts the cost of producing the ___?______ 399th 301st 300th 201st 299th  yard.
(c) Compare

C'(300)

with the cost of manufacturing the 301st yard of fabric. (Round your answers to four decimal places.)The cost of manufacturing the 301st yard of fabric is

C(301) − C(300) = ___?______− 10,500 ≈ ______?_____ ,

which is approximately

C'(300).

Answer 1