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JEE Main20254 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

Let f be a differentiable function on R such that f (2) = 1 , f^ (2)=4 . Let _ x 0 (f(2+x))^ 3 / x =e^ . Then the number of times the curve y=4 x^3-4 x^2-4( -7) x- meets x -axis is :-

Options

  1. A2
  2. B1
  3. C0
  4. D3

Correct answer

A. 2

Step-by-step solution

aligned & _ x 0 (f(2+x))^ 3 x & _ e ^ x 0 (f(2+x)-1) 3 x & e ^ 3 f^ (2) =(e)¹²=(e)^a a=12 & y=4 x^3-4 x^2-4(a-7) x-a & y=4 x^3-4 x^2-20 x-12 & roots x=-1,-1,3 & option (1) aligned

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