CBSE 2026 · Region 4 · Set 1 · Q23 · 2 marks
Find the values of x for which $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{x}}, \mathrm{x}>0$ is increasing.
Marking-scheme solution
$\displaystyle f^{\prime}(x)=x^{x}(1+\log x)$
Put, $\displaystyle f^{\prime}(x)=0 \Rightarrow x^{x}(1+\log x)=0$
As $\displaystyle x^{x}>0$ for $\displaystyle x>0,(1+\log x)=0 \Rightarrow x=\dfrac{1}{e}$
$\displaystyle \therefore f(x)$ is increasing when $\displaystyle x>\dfrac{1}{e}$ or $\displaystyle x \in\left(\dfrac{1}{e}, \infty\right)$ or $\displaystyle x \in\left[\dfrac{1}{e}, \infty\right)$
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.