For which interval the given function $f\left(x\right)=-2x^3-9x^2-12x+1$ is decreasing?

Given, $f\left(x\right)=-2x^3-9x^2-12x+1$

$f^{\text{'}}\left(x\right)=-6x^2-18x-12$

To be decreasing $f^{\text{'}}\left(x\right)<0$

$\Rightarrow -6x^2-18x-12<0$

$\Rightarrow x^2+3x+2>0$

$\Rightarrow \left(x+2\right)\left(x+1\right)>0$

Therefore, either $x<-2$ or $x>-1$

$x\in \left(-1,\infty \right)$ or $\left(-\infty ,-2\right)$

Hence, option (d) correct.