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BITSAT2018MathematicsApplication of DerivativesActual

For which interval the given function f x = - 2 x 3 - 9 x 2 - 12 x + 1 is decreasing?

Options

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

Correct answer

D. - ∞ , - 2 or - 1 , ∞

Step-by-step solution

Given, f x = - 2 x 3 - 9 x 2 - 12 x + 1 f ' x = - 6 x 2 - 18 x - 12 To be decreasing f ' x < 0 ⇒ - 6 x 2 - 18 x - 12 < 0 ⇒ x 2 + 3 x + 2 > 0 ⇒ x + 2 x + 1 > 0 Therefore, either x < - 2 or x > - 1 x ∈ - 1 , ∞ or - ∞ , - 2 Hence, option (d) correct.

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