Given, $y=-x^{3}+3 x^{2}+2 x-27$
$\Rightarrow \frac{d y}{d x}=-3 x^{2}+6 x+2$
Let slope $z=\frac{d y}{d x}=-3 x^{2}+6 x+2$
Then,$\frac{d z}{d x}=-6 x+6$
For maximum or minimum put $\frac{d z}{d x}=0$
$\Rightarrow -6 x+6=0$
$\Rightarrow x=1$
Now, $\frac{d^{2} z}{d x^{2}}-6<0$
Thus, $z$ is maximum for $x=1$ and the maximum value of $z$ is given by
$z=-3+6+2=5$