# 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.

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

x2 = 1 x = ±1

When x = 1, y = x3 = (1)3 y = 1

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

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).

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