Posted by **Anonymous** on Saturday, October 16, 2010 at 9:27am.

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.

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

- Math - average rate problems(check + help) -
**Reiny**, Saturday, October 16, 2010 at 9:42am
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

- Math - average rate problems(check + help) -
**Ish**, Sunday, March 1, 2015 at 12:24pm
x is the number of items produced in thousands

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