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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

Let f x = ∫ 0 x ( t - 1 ) ( t - 2 ) 2 d t . If f x ≥ k for all x and for some k , then the set of exhaustive values of k is

Options

  1. A0 , ∞
  2. B0 , 2
  3. C1 , ∞
  4. D– ∞ , – 17 12

Correct answer

D. – ∞ , – 17 12

Step-by-step solution

x = 1 is a point of global minima of f x Minimum value of f x =   ∫ 0 1 t - 1 t - 2 2 d t = ∫ 0 1 t 3 - 5 t 2 + 8 t - 4 d t = - 17 12

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