Question

an accessories company finds that the cost in dollars, of producing x belts is given by c(x)=710 + 31x - 0.062x^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. c(x)= -\frac{710}{x^2}-0.062 when 177 belts have been produced, the average cost is changing at □ for each additional belt. (round to four decimal places as needed.)

Explanation:

Step1: Substitute x = 177

$C'(177)=-\frac{710}{177^{2}}- 0.062$

Step2: Calculate the value

$C'(177)=-\frac{710}{31329}-0.062\approx - 0.02266 - 0.062=-0.0847$

Answer:

$-0.0847$