The average cost for a company to produce $x$ units of a product is given by the function $A(x)=\frac{15 x+3125}{x}$. Use $A^{\prime}(x)$ to estimate the change in average cost as production goes from 250 units to 251 units.

Step 1 ：The average cost for a company to produce \(x\) units of a product is given by the function \(A(x)=\frac{15 x+3125}{x}\).

Step 2 ：We are asked to estimate the change in average cost as production goes from 250 units to 251 units. This is essentially asking for the derivative of the average cost function at x = 250, which represents the rate of change of the average cost at that production level.

Step 3 ：To find this, we first need to find the derivative of the average cost function, \(A(x)\), which is \(A^{\prime}(x)\).

Step 4 ：\(A^{\prime}(x) = 15/x - (15*x + 3125)/x^2\)

Step 5 ：Then we substitute x = 250 into \(A^{\prime}(x)\) to find the rate of change at that point.

Step 6 ：The result is -1/20, which means that the average cost decreases by 1/20 units as production goes from 250 units to 251 units.

Step 7 ：Final Answer: The change in average cost as production goes from 250 units to 251 units is \(\boxed{-\frac{1}{20}}\).