Find the points on the curve 6 y= x^3+2 at which ordinate is changing 8 times as fast as abscissa.

Differentiating both sides w.r.to t , we get $\displaystyle 6 \frac{d y}{d t}=3 \mathrm{x}^{2} \frac{d \mathrm{x}}{d t}$ $$6.8 \frac{d \mathrm{x}}{d t}=3 \mathrm{x}^{2} \frac{d \mathrm{x}}{d t} \Rightarrow \mathrm{x}= \pm 4 $$ Points are $\displaystyle (4,11)$ and $\displaystyle \left(-4,-\frac{31}{3}\right)$