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JEE Main202228 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

The function f x = x e x 1 - x , x ∈ R , is

Options

  1. Aincreasing in - 1 2 , 1
  2. Bdecreasing in 1 2 , 2
  3. Cincreasing in - 1 , - 1 2
  4. Ddecreasing in - 1 2 , 1 2

Correct answer

A. increasing in - 1 2 , 1

Step-by-step solution

Let f x = x e x 1 - x then f x is: Now f x = x e x 1 - x Differentiating both side w.r.t x we get, f ' x = x e x 1 - x 1 - 2 x + e x 1 - x = - e x 1 - x 2 x 2 - x - 1 = - e x 1 - x 2 x + 1 x - 1 Now finding critical point by equating f ' x = 0 We get, x = - 1 2   &   x = 1 ∴     f x is decreasing in - ∞ , - 1 2 ∪ 1 , ∞ And increasing in - 1 2 , 1

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