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.

The equation of the curve is given as: x ϵ (a, b)

The rate of change of the position of the particle with respect to time (t) is given by,

f' (x) > 0

x ϵ (a, b)

When the y-coordinate of the particle changes 8 times as fast as the x-coordinate i.e.,  f' (x) > 0

x ϵ (a, b)

f' (x) < 0

x ϵ (a, b)

y = f(x)            (x_o, y_o)           

When (x_o, y_o)

Hence, the points required on the curve are (4, 11) and y = f(x)