$\text{ Maximum slope of the curve }y=-x^3+3x^2+9x-27\text{ is }$

$\begin{array}{l}\text{ Slope }=\frac{dy}{dx}=m=-3x^2+6x+9\\ \frac{dm}{dx}=-6x+6\\ \frac{dm}{dx}=0\Rightarrow x=1\\ \frac{d^{2}m}{d{x}^2}=-6<0,\mathrm{\forall }x\\ x=1\text{ is point of maximum }\\ \text{ Max. slope }=-3(1{)}^2+6(1)+9=12\end{array}$