For the curve $y=7 x-x^3$, if $x$ increases at the rate of 4 units $/ \mathrm{sec}$. then at $x=2$,

Question

For the curve $y=7 x-x^3$, if $x$ increases at the rate of 4 units $/ \mathrm{sec}$. then at $x=2$, the slope of the curve is changing at

Professor PC Thomas Classes · Answer

Slope $m = 7 - 3x^2$. $\frac{dm}{dt} = -6x \frac{dx}{dt} = -6(2)(4) = -48 	ext{ units/sec}$.