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NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If f x = x - 4 x - 4 + t a n - 1 1 - 2 x 2 + x ,   ∀ 4 < x < 8 , then the value of f ′ 5 is equal to

Options

  1. A- 7 13
  2. B0
  3. C5 13
  4. D- 8 13

Correct answer

A. - 7 13

Step-by-step solution

f x = x - 4 2 + 2 2 - 2.2 x - 4 + t a n - 1 1 2 - x 1 + 1 2 . x f x = x - 4 - 2 2 + t a n - 1 1 2 - t a n - 1 x f x = 2 - x - 4 + t a n - 1 1 2 - t a n - 1 x ∵ x - 4 < 2 f &#x2032; x = &#x2212; 1 2 x &#x2212; 4 &#x2212; 1 1 + x 2 f &#x2032; 5 = &#x2212; 1 2 &#x2212; 1 1 + 25 = &#x2212; 14 26 = &#x2212; 7 13

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