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प्रश्न
A particle moves along the curve y = x2 + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?
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उत्तर
\[\text { Here, } \]
\[y = x^2 + 2x\]
\[ \Rightarrow \frac{dy}{dt} = \left( 2x + 2 \right)\frac{dx}{dt}\]
\[ \Rightarrow 2x + 2 = 1 \left[ \because \frac{dy}{dt} = \frac{dx}{dt} \right]\]
\[ \Rightarrow 2x = - 1\]
\[ \Rightarrow x = \frac{- 1}{2}\]
\[\text { Substituting x }=\frac{- 1}{2}\text { in y }= x^2 +2x, \text { we get }\]
\[y = \frac{- 3}{4}\]
\[\text { Hence, the coordinates of the point are } \left( \frac{- 1}{2}, \frac{- 3}{4} \right) .\]
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