A particle moves along the curve y = (2/3)x 3 + 1. Find the points on the curve at which the y - coordinate is changing twice as fast as the x - coordinate.

Question

Philoid · Accepted Answer

Given: a particle moves along the curve .

To find the points on the curve at which the y - coordinate is changing twice as fast as the x - coordinate.

Equation of curve is

Differentiating the above equation with respect to t, we get

When y - coordinate is changing twice as fast as the x - coordinate, i.e.,

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

⇒ x² = 1 ⇒ x = ±1

When x = 1,

When x = - 1,

Hence the points on the curve at which the y - coordinate changes twice as fast as the x - coordinate are and

A particle moves along the curve y = (2/3)x3 + 1. Find the points on the curve at which the y - coordinate is changing twice as fast as the x - coordinate.

A particle moves along the curve y = (2/3)x³ + 1. Find the points on the curve at which the y - coordinate is changing twice as fast as the x - coordinate.