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Application Of Derivatives

Question
CBSEENMA12035160
Wired Faculty App

Find the equation of all lines having 0 slope and that are tangent to the curve straight y equals fraction numerator 1 over denominator straight x squared minus 2 straight x plus 2 end fraction.

Solution

The equation of the curve is straight y space equals space fraction numerator 1 over denominator straight x squared minus 2 straight x plus 2 end fraction
therefore space space space space dy over dx space equals space fraction numerator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis. space 0 minus 1 left parenthesis 2 straight x minus 2 right parenthesis over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction space equals space fraction numerator negative 2 straight x plus 2 over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction therefore space space space space space slope space of space tangent space space equals space fraction numerator negative 2 straight x plus 2 over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction But space slope space of space tangent space space equals space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis given right parenthesis therefore space space space space space space space fraction numerator negative 2 straight x plus 2 over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction space equals space 0 space space space space space rightwards double arrow space space space space space minus 2 straight x plus 2 space equals space 0 space rightwards double arrow space space space space straight x space equals space 1 When space straight x space equals space 1 comma space space space straight y space equals space fraction numerator 1 over denominator 1 minus 2 plus 2 end fraction space equals space 1 therefore space space space space space point space is space left parenthesis 1 comma space 1 right parenthesis. therefore space space space space space equation space of space tangent space left parenthesis 1 comma space 1 right parenthesis space with space slope space 0 space is space space space space space space space space space space space space space space space space space straight y minus 1 space equals space 0 left parenthesis straight x minus 1 right parenthesis space space space space or space space space space straight y minus 1 space equals space 0

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