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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Paragraph: Consider the function defined implicitly y^2+y-x=2 on various intervals on the real line. If y (- ,- 1 2 ) , the equation implicitly defines a unique real valued differentiable function y =f( x ) . On the basis of above informations, answer the following questions. Question: The value of f "(4) is -

Options

  1. A2 125
  2. B125 2
  3. C1 5
  4. D1 125

Correct answer

A. 2 125

Step-by-step solution

aligned & y^2+y-x=2 2 y d y d x + d y d x =1 & d y d x = 1 2 y+1 aligned d y d x = 1 2 y+1 put x=4 y=2,-3 aligned & y (- ,- 1 2 ) y=-3 & . dy dx |_ x=4 = . 1 2 y+1 |_ y=-3 =- 1 5 aligned Now (1+2 y) d^2 y d x^2 +2 ( d y d x )^2=0 . d ^2 y dx ^2 |_ x =4 = 2 125 f^ (4)= 2 125

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