Average Cost

[xamber]

The average cost for a company to produce x units of a product is given by the function
A(x) = (13x + 100) / x

Use A'(x) to estimate the change in average cost as production goes from 100 units to 101 units.

 

[Deleted member 4993]

The average cost for a company to produce x units of a product is given by the function
A(x) = (13x + 100) / x

Use A'(x) to estimate the change in average cost as production goes from 100 units to 101 units.

What does the value of the derivative of a function A'(x), at a point x =xo mean [in the context of the function A(x)]?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[HallsofIvy]

I thought your attachment would show your work. Instead it just shows the problem again.

You are give the function \(\displaystyle A= \frac{13x+ 1}{x}\)
and the first thing you are asked to do is find the derivative, A'.
Have you done that?

There are two ways to find the derivative of A:
1) use the quotient rule
2) write A as \(\displaystyle A= (13x+ 1)x^{-1}\) and use the product rule.

Do you know the "quotient rule" or the "product rule"?

The quotient rule says that (u/v)'= (u'v- uv')/v^2.
The product rule says that (uv)'= u'v+ uv'.

Of course the derivative of 13x+ 1 is the constant, 13, the derivative of x is 1, and the derivative of \(\displaystyle x^{-1}\) is \(\displaystyle -x^{-2}\).