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For the function f(x) = x^1/x, x > 0, which of the following are correct? (A) x = 0 is the only point where extremum may occur. (B) The given…

CUET UG 2025 — Mathematics Calculus

2025mcqmedium

For the function f(x)=x1/xf(x) = x^{1/x}f(x)=x1/x, x>0x > 0x>0, which of the following are correct?

(A) x=0x = 0x=0 is the only point where extremum may occur.

(B) The given function is maximum at x=ex = ex=e.

(C) The function has no extreme value for x>0x > 0x>0.

(D) The maximum value of the function f(x)f(x)f(x) is e1/ee^{1/e}e1/e.

Choose the correct answer from the options given below:

Official previous-year question

Held on 19 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (A), (B) and (D) only

  2. B

    (A) and (C) only

  3. C

    (C) and (D) only

  4. D

    (B) and (D) only

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