Question

The cost function for production of a commodity is

C(x) = 352 + 29x − 0.06x² + 0.0001x³.

(a) Find C'(100).


Interpret

C'(100).

This is the cost of making 100 items.This is the rate at which costs are increasing with respect to the production level when x = 100.    This is the amount of time, in minutes, it takes to produce 100 items.This is the rate at which the production level is decreasing with respect to the cost when x = 100.This is the number of items that must be produced before the costs reach 100.

(b) Find the actual cost of producing the 101st item. (Round your answer to the nearest cent.)
$

Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below.

C(x) = 5000 + 2x + 0.03x² + 0.0002x³

Answer 1