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: \(\boxed{7.7/x - (7.7x + 113)/x^2}\)