The interval on which the function f(x)=2 x^3+9 x^2+12 x-1 is dec… - Vidyadip

MCQ

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

A
$[-1, \infty)$
✓
$[-2,-1]$
C
$(-\infty,-2]$
D
$[-1,1]$

✓

Answer

Correct option: B.

$[-2,-1]$

(b) : $f(x)=2 x^3+9 x^2+12 x-1$
$
f^{\prime}(x)=6 x^2+18 x+12=6\left(x^2+3 x+2\right)=6(x+2)(x+1)
$
For decreasing function, $f^{\prime}(x) \leq 0$
$
\begin{array}{l}
\therefore \quad 6(x+2)(x+1) \leq 0 \\
\Rightarrow \quad(x+2)(x+1) \leq 0 \Rightarrow-2 \leq x \leq-1
\end{array}
$

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