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The possible value of the ordered triplet a , b , c such that the function f x = x 3 + a x 2 + b x + c is a monotonic function is

Options

  1. A2,1 , 3
  2. B1 , - 1,3
  3. C2,2 , 4
  4. D2 , - 2,1

Correct answer

C. 2,2 , 4

Step-by-step solution

f x = x 3 + a x 2 + b x + c f ' x = 3 x 2 + 2 a x + b ≥ 0 ,   ∀ x ∈ R D ≤ 0 4 a 2 - 12 b ≤ 0 a 2 ≤ 3 b From the given options, 2, 2 , 4 satisfies the above condition

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