1 Answer
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).
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