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Application Of Derivatives

Question
CBSEENMA12034971
Wired Faculty App

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007 x – 0.003 x2 + 15 x + 4000.
Find the marginal cost when 17 units are produced.

Solution

Here straight C left parenthesis straight x right parenthesis space equals space 0.07 space straight x cubed minus space 0.003 space straight x squared space plus space 15 straight x plus space 4000
therefore space space space space space straight C space equals space 0.007 space straight x cubed minus space 0.003 space straight x squared plus space 15 straight x space plus space 4000
Marginal cost     equals space dC over dx space equals space 3 left parenthesis 0.007 right parenthesis space straight x squared minus space 2. space left parenthesis 0.003 right parenthesis space straight x space plus space 15 
                         equals space 0.021 space straight x squared minus space 0.006 space straight x space plus space space 15
When x = 17,   marginal cost  = (0.021) (17)2 - (0.006) (17) + 15
                              equals space 0.021 space cross times space 289 space minus space 0.006 space cross times space 17 space plus space 15 equals space 6.069 space minus space 0.102 space space plus space 15 space equals space Rs space 20.967

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