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प्रश्न
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.
उत्तर
\[\text { According to the question },\]
\[\frac{dy}{dt} = 3\frac{dx}{dt}\]
\[\text { Now,} \]
\[y = x^3 \]
\[ \Rightarrow \frac{dy}{dt} = 3 x^2 \frac{dx}{dt}\]
\[ \Rightarrow 3\frac{dx}{dt} = 3 x^2 \frac{dx}{dt}\]
\[ \Rightarrow x^2 = 1\]
\[ \Rightarrow x = \pm 1\]
\[\text { Substituting x }=\pm1 \text { in y }= x^3 , \text { we get }\]
\[y = \pm 1\]
\[\text { So the points are }\left( 1, 1 \right)\text { and }\left( - 1, - 1 \right).\]
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