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MHT CET2019Evening ShiftMathematicsApplication of DerivativesActual

The function f x = x 3 - 3 x is….

Options

  1. AIncreasing in - ∞ , - 1 ∪ 1 , ∞ and decreasing in - 1,1
  2. BIncreasing in 0 , ∞ and decreasing in - ∞ , 0
  3. CDecreasing in 0 , ∞ and increasing in - ∞ , 0
  4. DDecreasing in - ∞ , - 1 ∪ 1 , ∞ and increasing in - 1,1

Correct answer

A. Increasing in - ∞ , - 1 ∪ 1 , ∞ and decreasing in - 1,1

Step-by-step solution

We have, function f x = x 3 - 3 x &#8658; f ' x = 3 x 2 - 3 = 3 x + 1 x - 1 Here, f ' x > 0 i n - ∞ , - 1 ∪ 1 , ∞ and f ' x < 0 in (-1, 1). ∴ f x is increasing in - ∞ , - 1 , ∪ 1 , ∞ and decreasing in (-1, 1).

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