Let (2 α, α) be the largest interval in which the function f(t)=(|t+1|)/t^2, t<0, is strictly decreasing. Then the local maximum value of the…

Let $\displaystyle (2 \alpha, \alpha)$ be the largest interval in which the function $\displaystyle f(t)=\frac{|t+1|}{t^2}, t<0$, is strictly decreasing. Then the local maximum value of the function $\displaystyle g(x)=2 \log _{\mathrm{e}}(x-2)+\alpha x^2+4 x-\alpha, x>2$, is $\displaystyle \_\_\_\_$