MathsJEE Main 24 Jan 2026, Shift 1·Q24·Numerical·Moderate

Applications of Derivatives · Monotonicity and local maxima

Let

(2\alpha, \alpha)

be the largest interval in which the function

f(t) = \dfrac{\lvert t + 1\rvert}{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 .

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