The marginal cost of a product is modeled by

Question

dC/dx=14/(14x+3)^-1/3
where x is the number of units. When x = 15, C = 160.
(a) Find the cost function. (Round your constant term to two decimal places.)
C =
Incorrect: Your answer is incorrect.

(b) Find the cost of producing 30 units. (Round your answer to two decimal places.)
$

Answer 1

a)

 

In any case, you need to find the anti-derivative of the function dC/dx.  This will give you the function C(x).   Since we are dealing with indefinite integrals, your function C(x) will have an arbitrary constant added to the end.

 

Once you have your indefinite integral (function C(x)), use the initial value condition   C(15) = 160  , to find the value of the arbitrary constant.

 

You will then have your actual cost function.

 

 

b)

 

Evaluate C(30).