CBSE 2023 · Region 1 · Set 2 · Q23 · 2 marks
Find the sub-intervals in which $\displaystyle \mathrm{f}(\mathrm{x})=\log (2+\mathrm{x})-\frac{\mathrm{x}}{2+\mathrm{x}}, \mathrm{x}>-2$ is increasing or decreasing.
Marking-scheme solution
$$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{2+\mathrm{x}}-\frac{2}{(2+\mathrm{x})^{2}}=\frac{\mathrm{x}}{(2+\mathrm{x})^{2}}Sign of $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})$
$\displaystyle \mathrm{f}(\mathrm{x})$ is decreasing in ( $\displaystyle -2,0$ )
and increasing in ( $\displaystyle 0, \infty$ )
$\displaystyle \mathrm{f}(\mathrm{x})$ is decreasing in ( $\displaystyle -2,0$ )
and increasing in ( $\displaystyle 0, \infty$ )Application of DerivativesIncreasing and Decreasing FunctionsApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.