Question

For the given cost function C(x), find the oblique asymptote of the average cost function C(X), C(x)=14,000+94x+0.03x^2

Answer 1

Answer: y = 0.03x + 94

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Explanation:

Lets define A(x) to be the average cost function where 
A(x) = C(x)/x
basically you divide the given cost function C(x) by the number of units produced (x)

Dividing C(x) over x leads to:
A(x) = C(x)/x
A(x) = (14000+94x+0.03x^2)/x ... substitution
A(x) = (0.03x^2+94x+14000)/x ... rearrange terms
A(x) = (0.03x^2)/x+(94x)/x+(14000)/x ... break up the fraction
A(x) = 0.03x + 94 + (14000/x) ... simplify

If x were to head off to infinity, then the portion 14000/x approaches 0. 

So this is why the oblique asymptote is y = 0.03x + 94

Basically, in the long run, the average cost will approach y = 0.03x + 94