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+4 x-\alpha, x. > 2, is \_\_\_\_ [24 jan 2026 Shift 1]

Application of Derivatives Part 3

Section: Mathematics

Question : 2 of 30

Marks: +1, -0

Let (2α,α) be the largest interval in which the function f(t)=‌

|t+1|

,t<0, is strictly decreasing. Then the local maximum value of the function g(x)=2loge(x−2)+αx2+4x−α,x.>2, is ____

[24 jan 2026 Shift 1]

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