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Question 310013
JEE Mathematics · Hard

Application of Derivatives: JEE Advanced MCQ

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JEE AdvancedHardQuestion 310013

Question

For f(x) = x^x (x > 0), the minimum occurs at:
  1. A
    x = 1/e
    Correct
  2. B
    x = e
  3. C
    x = 1
  4. D
    x = 0

Correct answer

x = 1/e

Explanation

f(x) = x^x → ln f = x ln x → f'/f = ln x + 1 → f'(x) = x^x(ln x + 1) = 0 → ln x = −1 → x = 1/e. f'' > 0 at x = 1/e → minimum.

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