A point is moving on the curve $y=x^3-3 x^2+2 x-1$ and the $y$-coordinate of the point is increasing at the rate of 6 units per second. When the point is at $(2,-1)$, the rate of change of $x$-coordinate of the point is

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Aicharya · Accepted Answer

Since, $y=x^3-3 x^2+2 x-1$ Now, $\frac{d y}{d t}=3 x^2 \frac{d x}{d t}-\frac{6 x d x}{d t}+\frac{2 d x}{d t}$ $\begin{aligned} & \Rightarrow \frac{d y}{d t}=\left(3 x^2-6 x+2ight) \frac{d x}{d t} 	ext { at }(2,-1) \ & \Rightarrow 6=(3 	imes 4-6 	imes 2+2) \frac{d x}{d t} \Rightarrow \frac{d x}{d t}=\frac{6}{2}=3\end{aligned}$

A point is moving on the curve $y=x^3-3 x^2+2 x-1$ and the $y$-coordinate of the point is increasing at the…

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