Question

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

• A. 0
• B. 12
• C. 16
• D. 32

Answer 1

Answer: (B)

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