A particle moves along the curve $6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

Question

$\begin{array}{1 1} \big(-4,\frac{-31}{3}\big)\; and (4,11) \\ \big(-4,\frac{31}{3}\big)\; and\;(4,11) \\\big(-4,\frac{-31}{3}\big)\; and \;(-4,11) \\ \big(-4,\frac{-31}{3}\big)\; and \;(4,-11) \end{array}$