Applications to Economics

[mathstresser]

The marginal cost function C'(x) was defined to be the derivative of the cost function. If the marginal cost of manufacturing x meters of fabric is C'(x)=5-.008x+.000009x^2 (measured in dollars per meter) and the fixed start-up scost is C(0)=$20,000, use the Net Change Theorem to find the cost of producing the first 2000 units.

The Net Change Theorem is F'(x)= f(b)-f(a)



I found that C(x)= 5x-.004x^2+.00000x^3+20,000

I get
C(2000)=70000

But the answer should be $38,000.

What am I doing wrong?

 

[Guest]

You have set up the cost equation correctly
C(x)= 5x-.004x^2+.000003x^3+20,000

and when x = 2000 is used the answer is $38 000.

I can only assume that you are doing some of the steps incorrect.
Do the problem as 4 expaned parts ie

5x = 5 (2000) = 10000

- .004 x^2 = - .004 ( (2000)^2) = - .004 ( 4000000) = -16 000

and so on.....

 

[mathstresser]

THANK YOU!