Find the marginal average cost function if cost and revenue are given by $C(x)=113+7.7 x$ and $R(x)=6 x-0.04 x^{2}$.
The marginal average cost function is $\bar{C}^{\prime}(x)=$
Answer
Final Answer: \(\boxed{7.7/x - (7.7x + 113)/x^2}\)
Step 1 ：Given the cost function is \(C(x)=113+7.7 x\) and the revenue function is \(R(x)=6 x-0.04 x^{2}\).
Step 2 ：The average cost function is the total cost function divided by the quantity of output, or \(C(x)/x\).
Step 3 ：Substitute the given cost function into the average cost function, we get \(\bar{C}(x) = (113+7.7 x)/x\).
Step 4 ：The marginal average cost function is the derivative of the average cost function.
Step 5 ：Take the derivative of the average cost function, we get \(\bar{C}^{\prime}(x)=7.7/x - (7.7x + 113)/x^2\).
Step 6 ：Final Answer: \(\boxed{7.7/x - (7.7x + 113)/x^2}\)
