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

The marginal cost of producing the xth box of

24chrim

21.01.2022

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

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bartekzelazek5083

02.04.2021

frankly yes, because when you want inverse a function you must inverse it with line x=y

so when you inverse a function Df and Rf will convert together!

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