Question

A point is moving on $y=-2x^2$. The $x$ coordinate of the point is decreasing at the rate of $5$ units per second. Find the rate at which the $y$ coordinate of the point is changing when the point is at $(1,2)$.

Answer 1

$y=-2x^2$

Differentiating w.r.t ${}^{\prime }{t}^{\prime }$ , we get

$\frac{dy}{dt}=-4x\frac{dx}{dt}$

as $\frac{dx}{dt}=-5$ and $x=1$ and $y=2$ , we get

Change of $y=\frac{dy}{dt}=(-4)\left(1\right)(-5)=20$ unit/second