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)

$\frac{d y}{d x}=-3x^{2}+6x-4=Z\left(l e t\right)$
For maximum value of $Z,$
$\frac{d Z}{d x}=0$
$-6x+6=0$
$x=1$
$\left(\frac{d^{2} Z}{d x^{2}}\right)=-6 < 0$ so, maxima occurs at $x=1$
$Z_{m a x}=-3+6-4=-1$