The total cost, c, in dollars of operating a factory that produces kitchen utensils is C(x)=0.5x^2+40x+8000, where x is the number of items produced in thousands.

Question

a)Determine the marginal cost of producing 5000itmes and compare this with the actual cost of producing the 5001st item.
Ans: C'(5)= 5+40=45 and the comparison is C(5.001)-c(5)=-.045

b) The average cost is found by dividing the total cost by the number of items produced. Determine the average cost of producing 5000items.
Ans: avg cost = total cost/5000
=$1.64

c)Determine the rate of change of the average cost of producing 5000 items. Interpret this value.
Ans: i tried to finding the derivative of the avg cost but i don't get the required ans -0.32

Answer 1

c) (unless I am not reading this correctly)

according to the definition
avg(x) = (0.5x^2+40x+8000)/x
= .5x + 40 + 8000/x

avg '(x) = .5 - 8000/x^2

avg '(5000) = .5 - 8000/5000^2 = .4998

Answer 2

x is the number of items produced in thousands