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clementine poppy de vere drummond - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 f(x) = \frac{4v}{(v - 1)^2}

📌 Let \(g(v) = \frac{4v}{(v - 1)^2}\). Find maximum on \(v \in (1, 2]\).

📌 Take derivative:

📌 g'(v) = \frac{4(v - 1)^2 - 4v \cdot 2(v - 1)}{(v - 1)^4} = \frac{4(v - 1)[(v - 1) - 2v]}{(v - 1)^4} = \frac{4(-v - 1)}{(v - 1)^3}

📌 For \(v > 1\), \(g'(v) < 0\), so \(g(v)\) is decreasing on \((1, 2]\). Hence, maximum at \(v \to 1^+\)? But let’s check value at endpoint.

📌 Wait — since derivative is negative, function decreases from \(v = 1^+\) to \(v = 2\), so maximum occurs as \(v \to 1^+\), but \(v > 1\), and we want finite maximum.

📌 But observe: as \(v \to 1^+\), g(v) → ∞? Let’s test:

📌 At \(v = 1.1\), \(g = 4(1.1)/(0.1)^2 = 4.4 / 0.01 = 440\)

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