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GATE 2025 BT – Question 14

Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 1 mark · Multiple choice

The minimum value of the function $f(x) = x + \frac{4}{x}$ for $x > 0$ is

  1. 1
  2. 2
  3. 3
  4. 4

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Correct answer: (D) 4

Explanation

$f'(x) = 1 - \frac{4}{x^2} = 0$ gives $x = 2$, and $f''(2) > 0$ so it is a minimum with $f(2) = 2 + 2 = 4$. (This also follows from AM-GM.)