Interpretation - Cost and Inverse

[johnjones]

The cost (dollars) of making x units of a good is modeled by
C(x) = 32x^2+400x/(x+5) (x>=0).

Evaluate lim x->infinity C(x)/x [with units] and interpret what it means.
What does C^-1(1000) mean? Calculate it.

Please help . thx.

I think it's infinity over infinity type. But if I'm given C(x), how do I find C(x)/x? For infinity over infinity, do I expand, factor?

 

[stapel]

When you divide "(quadratic)/(linear)" by "x", you'll get "(quadratic)/(quadratic)". That is, the rational expression will have the same degree in the numerator and the denomintor. Since "the limit, as x goes to infinity" is the same as "the horizontal asymptote", you don't even need calculus to figure out the answer to this. Just use what you know from back in algebra.

Eliz.

 

[johnjones]

When you divide "(quadratic)/(linear)" by "x", you'll get "(quadratic)/(quadratic)". That is, the rational expression will have the same degree in the numerator and the denomintor. Since "the limit, as x goes to infinity" is the same as "the horizontal asymptote", you don't even need calculus to figure out the answer to this. Just use what you know from back in algebra.

Eliz.

What does C^-1(1000) mean?
How would I interpret what inverse of C means? I know it can't mean average cost, b/c that's C.
So I guess the answer is positive infinity units or something (for the horizontal asym) :?:

 

[Daniel_Feldman]

C^-1(1000) is the inverse of C at 1000.


Think of a function f(x). It's inverse is denoted by f^-1(x).



In this case, you're looking for the value of x when the cost (C) is equal to 1000.