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CUET · MATHS · PYQ PAPER 2025

The function \(f(x)=\frac{x}{3}+\frac{3}{x}\) is increasing in the interval:

  1. A \((-\infty,-3) \cup(3, \infty)\)
  2. B \((-3,0) \cup(0,3)\)
  3. C \((-\infty, \infty)\)
  4. D \((0, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((-\infty,-3) \cup(3, \infty)\)

Step-by-step Solution

Detailed explanation

\(f'(x) = \frac{1}{3} - \frac{3}{x^2}\) \(\frac{1}{3} - \frac{3}{x^2} > 0\) \(\frac{1}{3} > \frac{3}{x^2}\) \(x^2 > 9\) \((x-3)(x+3) > 0\) \(x \in (-\infty, -3) \cup (3, \infty)\)