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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Paragraph: Let y=f(x) be a differentiable function passing through (1,0) . Let slope of the tangent at the point (x, f(x)) be m₁ and slope of line joining the point and origin be m₂ . Also | (m₁+m₂ ) x |= 2 1 . If f₁(x) and f₂(x) are 2 function satisfying the above property where f₁(x) is an algebraic function and f₂(x) is a transcendental function. Question: The value of _ -1 ^1 (f₁(x)+ 1 4 x ) d x is equal to:

Options

  1. A0
  2. B4
  3. C8
  4. D12

Correct answer

A. 0

Step-by-step solution

array cl Case-I : & (m₁+m₂ ) x =2 & m₁+m₂=x^2 & f^ (x)+ f(x) x =x^2 array aligned & I.F. =e^ x =x & x f(x)= x^4 4 +C & At (1,0) C= -1 4 & f₁(x)= x^3 4 - 1 4 x ...(1) & Case-II : (m₁+m₂ ) x =-2 & m₁+m₂= 1 x^2 & f^ (x)+ f(x) x = 1 x^2 & I.F. =x & aligned aligned & x f(x)= x+C At (1,0) C & =0 & f₂(x)= x x aligned

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