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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 5 · Set 3 · Q23
Determine the interval(s) in which f ( x )=x/3+3/x, x ≠ 0 is increasing.
Determine the interval(s) in which $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{3}+\frac{3}{\mathrm{x}}, \mathrm{x} \neq 0$ is increasing.
Marking-scheme solution
$\displaystyle f^{\prime}(x)=\dfrac{1}{3}-\dfrac{3}{x^{2}}$
$\displaystyle f^{\prime}(x)=0$ gives $\displaystyle x=3,-3$
Sign of $\displaystyle f^{\prime}(x)$:
$\displaystyle f(x)$ is increasing in $\displaystyle (-\infty,-3) \cup(3, \infty)$ or $\displaystyle (-\infty,-3] \cup[3, \infty)$
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