CBSE 2026 · Region 5 · Set 2 · Q23 · 2 marks
Determine the interval(s) in which $\displaystyle \mathrm{f}(\mathrm{x})=5 \mathrm{x}^{3 / 2}-3 \mathrm{x}^{5 / 2}, \mathrm{x}>0$ is increasing.
Marking-scheme solution
$\displaystyle f^{\prime}(x)=\dfrac{15 x^{\frac{1}{2}}}{2}-\dfrac{15 x^{\frac{3}{2}}}{2}$
$\displaystyle f^{\prime}(x)=0$ gives $\displaystyle x=1$ as $\displaystyle x>0$
Sign of $\displaystyle f^{\prime}(x)$:
$\displaystyle f(x)$ is increasing in $\displaystyle (0,1)$ or $\displaystyle (0,1]$
Application of DerivativesIncreasing and Decreasing FunctionsApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.