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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If the function f x = x 3 - 3 a x has a local minimum at x = λ λ ≥ 4 and a ∈ 10,18 , then the sum of all the possible integral values of a is

Options

  1. A50
  2. B112
  3. C51
  4. D16

Correct answer

C. 51

Step-by-step solution

f ′ x = 3 x 2 − 3 a = 3 x - a x + a ∴ f x has a local minimum at x = a ⇒ a ≥ 4 ⇒ a ≥ 16 ∴ ‘ a ’ can be 16,17,18

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