Math Question: The average cost for a company to produce x units of a product is given by the function A(x) = (13x + 100) / x Use A'(x) to estimate the change in average cost as production goes from 100 units to 101 units.

(1) If A(x) = 13 + 100/x , then A'(x) = -100/(x^2). A'(100) = -100/10000 = -0.01. We can estimate the change in average cost as x: 100 -> 101 by assuming ?A (x: 100->101) = A'(x=100) * ?x = -0.01 * 1 = -0.01. So the change in average cost decreased by about 1 cent. (2) Checking this by actually doing A(101)-A(100): A(101)-A(100) = (100/101)-(100/100) = 0.9901...-1 = approximately -0.01. Sounds about right.
Answered On 02/22/2021 00:19

calculate A(x) for each value 100 and 101. (100,14), (101,13.99), then calculate the slope which is the rate of change. (101-100)/(13.99-14)=1/(-.01)=-100
Answered On 02/26/2021 07:39