Q26 of 78 Page 13

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.

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


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