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# Rates of Change : Cost and Marginal Cost

3.) A company determines that the cost in dollars to the manufacture x cases of the dvd "math caught in embarrassing moments" is given by C(x) = 100 + 15x - x^2, (0< or = x < or = 7)

a.) Find the average rate of change of the cost per case for the manufacturing between 1 and 5 cases [ review ex. 2a]

So on the average, the cost increased at the rate of _______ per case when the production increased from 1 to 5 cases.

b.) Find the instantaneous rate of change of cost with respect to the number of cases produced when just one case is produced. [ review ex. 2b]

When 1 case is manufactured , in the cost is ___________ at the rate of ______ per case . (marginal cost)

c.) Find the marginal cost when 5 cases are made.

When 5 cases are manufactured , the cost is increasing at the rate of \$________ per case: that is the marginal cost when x+5 is \$__________. Notice that as the number of items produced goes up, the marginal cost goes down.

#### Solution Summary

Rates of Change of Cost and Marginal Cost are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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