Question

The marginal cost of producing the xth box of CDs is given by 9 − x/(x2 + 1)2. The total cost to produce two boxes is $1,100. Find the total cost function C(x).

Answer 1

Answer:

C(x)=$9x+\frac{1}{2(x^2+1)}+1081.9$

Step-by-step explanation:

We are given that

$C'(x)=9-\frac{x}{(x^2+1)^2}$

Total cost function

C(x)=$\int(9-\frac{x}{(x^2+1)^2})dx$

Let $x^2+1=t$

$2xdx=dt$

$xdx=\frac{1}{2}dt$

$\int\frac{x}{(x^2+1)^2}dx=\int\frac{1}{2t^2}dt=-\frac{1}{2t}=-\frac{1}{2(x^2+1)}$

Substitute the value

$C(x)=9x+\frac{1}{2(x^2+1)}+C$

Substitute x=2

$C(2)=9(2)+\frac{1}{2(5)}+C$

$1100=18+\frac{1}{10}+C$

$1100-18-\frac{1}{10}=C$

$1082-0.1=C$

$1081.9=C$

Total cost function, C(x)=$9x+\frac{1}{2(x^2+1)}+1081.9$