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The maximum value of f x = log ⁡ x x ( x ≠ 0 , x ≠ 1 ) is

Options

  1. Ae
  2. B1 e
  3. Ce 2
  4. D1 e 2

Correct answer

B. 1 e

Step-by-step solution

f x = log ⁡ x x f ′ ( x ) = x 1 x − log x x 2 = 1 − log x x 2 f ′ ( x ) = 0 ⇒ 1 − log x x 2 = 0 ⇒ log ⁡ x = 1 ⇒ x = e ⇒ Max value is f e = log ⁡ e e = 1 e

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