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BITSAT2017MathematicsApplication of DerivativesActual

Let f x = - 2 x 3 + 21 x 2 - 60 x + 41 , then

Options

  1. Af x is decreasing in 2 , 5
  2. Bf x is decreasing in - ∞ , 2
  3. Cf x is increasing in - ∞ , 1
  4. Df x is increasing in - ∞ , 2

Correct answer

B. f x is decreasing in - ∞ , 2

Step-by-step solution

Given, f x = - 2 x 3 + 21 x 2 - 60 x + 41 On differentiating w.r.t. x , we get f ' x = - 6 x 2 + 42 x - 60 ⇒ f ' x = - 6 x 2 - 7 x + 10 ⇒ f ' x = - 6 x - 2 x - 5 ⇒ x < 2   or   x > 5 ,   f ' x < 0 i.e., f x is decreasing and 2 < x < 5 ,   f ' x > 0 i.e., f x is increasing

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