Question

The maximum slope of the curve $y=-x^3+3x^2-4x+9$ is

• A. $1$
• B. $-1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$\frac{dy}{dx}=-3x^2+6x-4=Z\left(let\right)$
For maximum value of $Z,$
$\frac{dZ}{dx}=0$
$-6x+6=0$
$x=1$
$\left(\frac{d^{2}Z}{d{x}^2}\right)=-6<0$ so, maxima occurs at $x=1$
$Z_{max}=-3+6-4=-1$