Question

A point is moving on $y=4-2x^2$. The x-coordinate of the point is decreasing at the rate of $5$ units per second. Then the rate at which y-coordinate of the point is changing when the point is at $(1,2)$ is.

• A. $5$ units/sec
• B. $10$ units/sec
• C. $15$ units/sec
• D. $20$ units/sec

Answer 1

Answer: (D)

$20$ units/sec

$y=4-2x^2$

$\frac{dy}{dt}=-2.2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=-4x.5$

At $(1,2),\frac{dy}{dt}=-4.5=-20unit/sec$

$\Rightarrow \left|\frac{dy}{dt}\right|=20unit/sec$