CBSE 2023 · Region 3 · Set 3 · Q24 · 2 marks
Find the points on the curve $\displaystyle 6 y=\mathrm{x}^{3}+2$ at which ordinate is changing $\displaystyle 8$ times as fast as abscissa.
Marking-scheme solution
Differentiating both sides w.r.to t , we get $\displaystyle 6 \frac{d y}{d t}=3 \mathrm{x}^{2} \frac{d \mathrm{x}}{d t}$6.8 \frac{d \mathrm{x}}{d t}=3 \mathrm{x}^{2} \frac{d \mathrm{x}}{d t} \Rightarrow \mathrm{x}= \pm 4Points are $\displaystyle (4,11)$ and $\displaystyle \left(-4,-\frac{31}{3}\right)$
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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.