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 ________.
