Question

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

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

Answer 1

The correct option is C $[-2,-1]$

Given: $f\left(x\right)=2x^3+9x^2+12x-1$
Differentiating both side warta $x$,

$\Rightarrow f^{\prime }\left(x\right)=6x^2+18x+12$
$\Rightarrow f^{\prime }\left(x\right)=6(x^2+3x+2)$
$\Rightarrow f^{\prime }\left(x\right)=6(x+2)(x+1)$

The sign scheme of $f^{\prime }\left(x\right)$ is

Clearly, $f^{\prime }\left(x\right)\le 0$ when $x\in [-2,-1]$
The interval in which function is decreasing is $x\in A[-2,-1]$
Hence, option (b) is correct.