CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=\frac{x}{3}+\frac{3}{x}\) is increasing in the interval:
- A \((-\infty,-3) \cup(3, \infty)\)
- B \((-3,0) \cup(0,3)\)
- C \((-\infty, \infty)\)
- D \((0, \infty)\)
Answer & Solution
Correct Answer
(A) \((-\infty,-3) \cup(3, \infty)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{1}{3} - \frac{3}{x^2}\) \(\frac{1}{3} - \frac{3}{x^2} > 0\) \(\frac{1}{3} > \frac{3}{x^2}\) \(x^2 > 9\) \((x-3)(x+3) > 0\) \(x \in (-\infty, -3) \cup (3, \infty)\)
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