For the curve y=5 x-2 x^3, if x increases at the rate of 2 units / s, then how fast is the slope of the curve changing when x=2?

\[y=5 x-2 x^{3} \] Given $\displaystyle \frac{d x}{d t}=2$ units $\displaystyle / \mathrm{s}$ slope of the curve $\displaystyle =\frac{d y}{d x}=5-6 x^{2}=m$ \[\frac{d m}{d t}=-12 x \frac{d x}{d t}=-12 x(2)=-24 x \] at $\displaystyle x=2, \frac{d m}{d t}=-24(2)=-48$ Hence,slope of curveis decreasing at the rate of $\displaystyle 48$