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JEE Main20204 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

Let f be a twice differentiable function on 1 , 6 , If f 2 = 8 , f ' 2 = 5 , f ' x ≥ 1 and f ' ' x ≥ 4 , for all x ∈ 1 , 6 , then :

Options

  1. Af 5 + f ' 5 ≤ 26
  2. Bf 5 + f ' 5 ≥ 28
  3. Cf ' 5 + f ' ' 5 ≤ 20
  4. Df 5 ≤ 10

Correct answer

B. f 5 + f ' 5 ≥ 28

Step-by-step solution

Given f ' x ≥ 1 ⇒     ∫ 2 5 f ' x d x ≥ ∫ 2 5 1 . d x ⇒ f x 2 5 ≥ x 2 5 ⇒ f 5 − f 2 ≥ 3 ⇒ f 5 ≥ 11 .... 1 Now f ' ' x ≥ 4 ⇒ ∫ 2 5 f ' ' x d x ≥ ∫ 2 5 4 d x = f ' x 2 5 ≥ 4 x 2 5 ⇒     f ' 5 − f ' 2 ≥ 12 ⇒     f ' 5 ≥ 17 .... 2 1 + 2 ⇒ f 5 + f ' 5 ≥ 28 .

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