Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

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