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: a particle moves along the curve y = x³.

To find the points on the curve at which the y - coordinate changes three times more rapidly than the x - coordinate

Equation of curve is y = x³

Differentiating the above equation with respect to t, we get

When y - coordinate changes three times more rapidly than the x - coordinate, i.e.,

Equating equation (i) and equation (ii), we get

Hence 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).