Question

If $y=6x-x^3$ and $x$ increases at the rate of $5$ units per second, the rate of change of slope when $x=3$ is

• A. $-90$ units/sec
• B. $90$ units/ sec
• C. $180$ units/sec
• D. $-180$ units/sec

Answer 1

Answer: (A)

$-90$ units/sec

Slope of tangent is, $m=\frac{dy}{dx}=6-3x^2$

$\Rightarrow \frac{dm}{dt}=0-6x\frac{dx}{dt}$, rate of change of slope $m$

$\therefore \frac{dm}{dt}{|}_{x=3}=-6\left(3\right)\left(5\right)=-90$ units/sec