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  4. The maximum slope of the curve y=-x3+3 x2+9 x-27 is

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Q. The maximum slope of the curve $y=-x^{3}+3 x^{2}+9 x-27$ is

Solution:

$y=-x^{3}+3 x^{2}+9 x-27$
$\Rightarrow $ slope $m=\frac{d y}{d x}=-3 x^{2}+6 x+9$
$\frac{d m}{d x}=-6 x+6=0$
$\Rightarrow x=1 \frac{d^{2} m}{d x^{2}}=-6<0$
Max slope $=- 3 + 6 + 9=12$