Question

an accessories company finds that the cost, in dollars, of producing x belts is given by c(x)=710 + 31x - 0.06x^2. find the rate at which average cost is changing when 177 belts have been produced. first, find the rate at which the average cost is changing when x belts have been produced. $overline{c}(x)=square$

Explanation:

Step1: Define average - cost function

The average - cost function $\bar{C}(x)=\frac{C(x)}{x}=\frac{710 + 31x-0.062x^{2}}{x}=\frac{710}{x}+31 - 0.062x$.

Step2: Differentiate average - cost function

Using the power rule, $\bar{C}'(x)=-\frac{710}{x^{2}}-0.062$.

Answer:

$-\frac{710}{x^{2}}-0.062$