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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 3 · Set 2 · Q25
Find the sub-interval of (0, ∞) in which f ( x )= x^2 e^- x is increasing.
Find the sub-interval of $\displaystyle (0, \infty)$ in which $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x}^{2} \mathrm{e}^{-\mathrm{x}}$ is increasing.
Marking-scheme solution
$\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x}^{2} \mathrm{e}^{-\mathrm{x}} \Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=\mathrm{x}(2-\mathrm{x}) \mathrm{e}^{-\mathrm{x}}$
Put $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})=0 \Rightarrow \mathrm{x}=0,2$
Hence, $\displaystyle \mathrm{f}(\mathrm{x})$ is increasing in $\displaystyle (0,2)$.
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.