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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 4 · Set 3 · Q23
Find the interval(s) for which the function f ( x )=x/3+3/x, x ≠ 0 is increasing.
Find the interval(s) for which the function $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{3}+\frac{3}{\mathrm{x}}, \mathrm{x} \neq 0$ is increasing.
Marking-scheme solution
$\displaystyle f^{\prime}(x)=\dfrac{1}{3}-\dfrac{3}{x^{2}}=\dfrac{x^{2}-9}{3 x^{2}}$
For increasing function, $\displaystyle f^{\prime}(x)=0 \Rightarrow x^{2}-9=0 \Rightarrow x=-3,3$
$\displaystyle \therefore f(x)$ is increasing on $\displaystyle x \in(-\infty,-3) \cup(3, \infty)$.
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