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Unformatted text preview: Math 1314 Day 3 Some Applications of the Derivative Section 11.4 Marginal Cost Suppose a business owner is operating a plant that manufactures a certain product at a known level. Sometimes the business owner will want to know how much it costs to produce one more unit of this product. The cost of producing this additional item is called the marginal cost . Suppose the total cost in dollars per week by ABC Corporation for producing its best selling product is given by . 4 . 3000 000 , 10 ) ( 2 x x x C + = We can find the actual cost of producing the 101 st item. The cost of producing the 101 st item can be found by computing the average rate of change, that is by computing 100 101 ) 100 ( ) 101 ( C C . Note that x h x x C h x C C C + + = ) ( ) ( ) ( 100 101 ) 100 ( ) 101 ( where x = 100 and h = 1. Suppose the total cost in dollars per week by ABC Corporation for producing its best selling product is given by . 4 . 3000 000 , 10 ) ( 2 x x x C + = Find ) 100 ( ' C and interpret the results. Example 1 : A company produces noisecanceling headphones. Management of the company has determined that the total daily cost of producing x headsets can be modeled by the function 000 , 15 135 03 . 0001 . ) ( 2 3 + + = x x x x C . Find the marginal cost function. Use the marginal cost function to approximate the actual cost of producing the 21 st , and 181 st headsets. Average Cost and Marginal Average Cost Suppose ) ( x C is the total cost function for producing x units of a certain product. If we divide this function by the number of units produced, x , we get the average cost function . We denote this function by ) ( x C . Then we can express the average cost function as x x C x C ) ( ) ( = . The derivative of the average cost function is called the marginal average cost....
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 Fall '08
 MARKS
 Derivative

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