Given a particle moves along the curve y = x^{3}.

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 = x^{3}

Differentiating the above equation with respect to t, we get

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

\( \dfrac{dy}{dt}=3\dfrac{dx}{dt}\) ...(ii)

The equating (i) and equation (ii)

When x = – 1, y = x^{3}

= (- 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).

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