A point is moving on $y=4-2 x^2$. The $x$-coordinate of the point is decreasing at the rate of 5…
A point is moving on $y=4-2 x^2$. The $x$-coordinate of the point is decreasing at the rate of 5 units/second. Then, the rate at which $y$ coordinate of the point is changing when the point is at $(1,2)$ is
5 unit/s
10 unit/s
15 unit/s
20 unit/s
Solution
Given equation of curve is
$
y=4-2 x^2
$
On differentiating both sides w.r.t. $t$, we get
$
\begin{aligned}
\frac{d y}{d t} & =-4 x \frac{d x}{d t} \\
\because \quad \frac{d x}{d t} & =-5, \text { point }(1,2) \\
\Rightarrow \quad \frac{d y}{d t} & =-4(1)(-5)=20 \text { unit/s }
\end{aligned}
$