Question

A particle moves along the curve 6y = x³ + 2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

Answer 1

Given,

6y = x³ +2

Differentiating w.r.t. t, we get

From question,

\(\frac{dy}{dt}=8.\frac{dx}{dt}\)

Hence, the required points are (4,11) and (- 4, \(\frac{-31}{3}\)).