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Application Of Derivatives

Question
CBSEENMA12035610
Wired Faculty App

If y = x4 – 10 and if x changes from 2 to 1.99, what is the approximate change in y?

Solution

Now,    δy is approximately equal to dy and 
Here,     straight y space equals straight x to the power of 4 minus 10                                dy space equals space dy over dx dx space equals space 4 straight x cubed dx
therefore space space space dy over dx space equals 4 straight x cubed                               equals space 4 left parenthesis 2 right parenthesis cubed space left parenthesis negative 0.01 right parenthesis space equals space minus 32 space cross times space 0.01 space equals space minus 0.32
                                           When space straight x space equals space 2 comma space space space straight y space equals left parenthesis 2 right parenthesis to the power of 4 space minus 10 space equals space 16 minus 10 space equals space 6
therefore space space space space straight x space changes space from space 2 space to space 1.99 space space space space space space space space space space space space space therefore space space space straight y space plus space δy space equals space 6 plus left parenthesis negative 0.32 right parenthesis space equals space 5.68 therefore space space space space straight x space equals space 2 comma space space space space space space δx space equals space dx space equals space minus 0.01 space space space space space space space space space therefore space space space straight y space changes space from space 6 space to space 5.68

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