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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: If y = h ( x ) is mirror image of y =f( x ) about the line 2 y +1=0 , then f^ ( x ₀ )+ h ^ ( x ₀ ) , where x ₀ (- 9 4 , ) is -

Options

  1. A2 x₀
  2. B2 2 f ( x ₀ )+1
  3. C2 (2 f (x₀ )+1 )^3
  4. D0

Correct answer

D. 0

Step-by-step solution

h ( x ) is mirror image of f( x ) in y =- 1 2 aligned & f( x )+ h ( x ) 2 =- 1 2 f( x )+ h ( x )=-1 & f^ ( x )+ h ^ ( x )=0 x (- 9 4 , ) aligned

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