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)

$f'(x) = 6x^2 + 18x + 12 = 6(x^2 + 3x + 2)$
$= 6 (x + 2) (x + 1)$
Since $f(x)$ is decreasing.
$\therefore f'(x) \le 0$
$\therefore (x + 2) (x + 1) \le 0$
$\Rightarrow x + 2 \ge 0$, $x + 1 \le 0$ 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]
$\Rightarrow x \in [-2, - 1]$