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.

Asked by Aaryan | 1 year ago |  88

##### Solution :-

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 - co-ordinate change three times more rapidly than the x - co-ordinate, that is

$$\dfrac{dy}{dt}=3\dfrac{dx}{dt}$$ ...(ii)

The equating (i) and equation (ii)

When x = – 1, y = x3

= (- 1)3

= y = – 1

Thus, 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).

Answered by Sakshi | 1 year ago

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