Question

The interval on which the function $f(x)=2x^3+9x^2+12x-1$ is decreasing in

• A. $[-1,\infty ]$
• B. $[-2,-1]$
• C. $[-\infty ,-2]$
• D. $[-1,1]$

Answer 1

Answer: (B)

$f^{\prime }(x)=6x^2+18x+12=6(x^2+3x+2)$
$=6(x+2)(x+1)$
Since $f(x)$ is decreasing.
$\therefore f^{\prime }(x)\le 0$
$\therefore (x+2)(x+1)\le 0$
$\Rightarrow x+2\ge 0$, $x+1\le 0$ or $x+2\le 0$, $x+1\ge 0$
$\Rightarrow x\ge -2$, $x\le -1$ or $x\le -2$, $x\ge 1$
$\Rightarrow -2\le x\le -1$ or $-1\le x<-2$ [not possible]
$\Rightarrow x\in [-2,-1]$