A particle moves along the curve y = x 3 . Find the points on the curve at which the y - coordinate changes three times more rapidly than the x - coordinate.

Question

Philoid · Accepted Answer

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).

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.

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.