Thank you for reporting, we will resolve it shortly
Q.
If the absolute maximum value of the function $f(x)=\left(x^2-2 x+7\right) e^{\left(4 x^3-12 x^2-180 x+31\right)}$ in the interval $[-3,0]$ is $f(\alpha)$, then:
$ f ^{\prime}( x )= e ^{\left(4 x ^3-12 x ^2-180 x +31\right)}\left(12\left( x ^2-2 x +7\right)( x +3)( x -5)+2( x -1)\right)$
$ \text { for } x \in[-3,0] $
$\Rightarrow f ^{\prime}( x ) < 0$
$f(x) $ is decreasing function on $ [-3, 0]$
The absolute maximum value of the function $f(x)$ is at $x=-3$
$\Rightarrow \alpha=-3$