Question

A particle moves along the curve y = x³. Find the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate.

Answer 1

Given as a particle moves along the curve y = x³.

As to find the points at the curve at which the y – coordinate changes three times more rapidly than the x – coordinate

The equation of curve is y = x³

Differentiate the above equation with respect to t, 

When y - co-ordinate change three times more rapidly than the x - co-ordinate, that is

dy/dt = 3(dx/dt) ...(ii)

The equating (i) and equation (ii)

When x = – 1, y = x³ = (- 1)³⇒ y = – 1

Thus, the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate are (1, 1) and ( – 1, – 1).