Question

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

• A. $5$
• B. $-5$
• C. $\frac{1}{5}$
• D. None of these

Answer 1

Answer: (A)

Given, $y=-x^3+3x^2+2x-27$
$\Rightarrow \frac{dy}{dx}=-3x^2+6x+2$
Let slope $z=\frac{dy}{dx}=-3x^2+6x+2$
Then,$\frac{dz}{dx}=-6x+6$
For maximum or minimum put $\frac{dz}{dx}=0$
$\Rightarrow -6x+6=0$
$\Rightarrow x=1$
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
$z=-3+6+2=5$