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

$(A)[-1,-2]\quad(B)[-2,-1]\quad(C)[-1,-2]\quad(D)[-1,1]$

Toolbox:
• Let $f(x)$ be a function defined on $(a,b)$. If $f'(x)<0$ for all $x \in (a,b)$ except for a finite number of points, where $f'(x)=0,$ then $f(x)$ is decreasing on $(a,b)$
Step 1
$f(x)=2x^3+9x^2+12x-1$
differentiating w.r.t $x$ we get,
$f'(x)=6x^2+18x+12$
If $f'(x)$ is decreasing $f'(x)<0$
$\Rightarrow 6x^2+18x+12<0$
$\Rightarrow 6(x^2+3x+2)<0$
$\Rightarrow 6(x+2)(x+1)<0$
This clearly implies that the given function is decreasing in the interval $[-2, -1]$
Hence B is the correct option.