Task 3. II variant.

For what values of the parameter $a$ does the function $y=\frac{8}{x^{2}+4 x+44}$ increase on the interval $[a-3 ; 3 a]?$
Solution. The function is increasing on the interval $(-\infty ;-2]$. The function will be decreasing on the segment $[a-3 ; 3 a]$ under the conditions

$\left\{\begin{array}{l}3 a \leq-2, \\ a-3<3 a\end{array} \Leftrightarrow \quad-\frac{3}{2}<a \leq-\frac{2}{3}\right.$.

Answer: $a \in\left(-\frac{3}{2} ;-\frac{2}{3}\right]$.