The average cost for a company to produce $x$ units of a product is given by the function $A(x)=\frac{11 x+1125}{x}$. Use $A^{\prime}(x)$ to estimate the change in average cost as production goes from 150 units to 151 units.
The change in average cost is approximately dollars.
Answer
Final Answer: The change in average cost as production goes from 150 units to 151 units is approximately \(\boxed{-\frac{1}{20}}\) dollars.
Step 1 ：The average cost for a company to produce \(x\) units of a product is given by the function \(A(x)=\frac{11 x+1125}{x}\).
Step 2 ：We are asked to estimate the change in average cost as production goes from 150 units to 151 units.
Step 3 ：This is essentially asking for the derivative of the average cost function at x=150, which represents the rate of change of the average cost at that point.
Step 4 ：To find this, we first need to find the derivative of the average cost function, \(A(x)\), which is given by \(A'(x)\).
Step 5 ：The derivative of the average cost function is \(A'(x) = 11/x - (11*x + 1125)/x^2\).
Step 6 ：Substitute x=150 into \(A'(x)\) to find the rate of change at that point.
Step 7 ：The change in average cost as production goes from 150 units to 151 units is approximately \(-\frac{1}{20}\) dollars.
Step 8 ：Final Answer: The change in average cost as production goes from 150 units to 151 units is approximately \(\boxed{-\frac{1}{20}}\) dollars.
