The cost in dollars of producing x units of a particular telephone is C(x) = x^2 - 2500.

Question

a.) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 103. Include units in your answer.

b.) Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.

Answer 1

a.) Average rate of change of C C_av = (C(103) - C(100))/(103 - 100) = (103² - 2500 - 100² + 2500)/3 = $203 per telephone.

b.) C'(x) = 2x is instantaneous cost.

At x = 100 C'(100) = 2·100 = $200 per thelephone.