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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The length of the longest interval in which the function f x = x 3 - 3 a 2 x + 4 is decreasing is ∀ a > 0

Options

  1. Aa
  2. B2 a
  3. C3 a
  4. D4 a

Correct answer

B. 2 a

Step-by-step solution

f ′ x = 3 x 2 − 3 a 2 = 3 x - a x + a ∴ f x decreases in x ∈ - a , a i.e. length = 2 a

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