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JEE Main202116 Mar 2021Evening ShiftMathematicsApplication of DerivativesActual

Let f be a real valued function, defined on R - - 1 , 1 and given by f x = 3 log e x - 1 x + 1 - 2 x - 1 . Then in which of the following intervals, function f x is increasing?

Options

  1. A- ∞ , - 1 ∪ 1 2 , ∞ - 1
  2. B- ∞ , ∞ - - 1 , 1
  3. C- 1 , 1 2
  4. D- ∞ , 1 2 - - 1

Correct answer

A. - ∞ , - 1 ∪ 1 2 , ∞ - 1

Step-by-step solution

f x = 3 log e x - 1 - 3 log e x + 1 - 2 x - 1 f ' x = 3 x - 1 - 3 x + 1 + 2 x - 1 2 f ' x = 4 2 x - 1 x - 1 2 x + 1 f ' x ≥ 0 ⇒    x ∈ - ∞ , - 1 ∪ 1 2 , 1 ∪ 1 , ∞ or - ∞ , - 1 ∪ 1 2 , ∞ - 1

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