Let be the largest interval in which the function is strictly decreasing. Then the local maximum value of the function is ________ . [2026]

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Solution

Q.
Let $(2 α, α)$ 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 $g (x) = 2 \log_{e} (x - 2) + α x^{2} + 4 x - α, x > 2,$ is ________ . [2026]

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