A particle moves along the curve 6y = x 3 +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

Question

Philoid · Accepted Answer

It is given that equation of the curve is 6y = x³ + 2.

The rate of change of the position of the particle with respect to time (t) is given by:

………….. (1)

When the y- coordinate of the particle changes 8 times as fast as the x – coordinate

then, we have,

So, putting the value in (1), we get,

So, when x = +4, then,

And

So, when x = -4, then,

Therefore, the points required on the curve are (4,11) are .