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Home » The maximum occurs at \(x = -\fracb2a\). - AMAZONAWS

The maximum occurs at \(x = -\fracb2a\). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Since \( x^2 \geq 0 \), we require:

📌 \frac{y + 1}{y - 1} \geq 0.

📌 Analyzing the sign of the expression:

📌 The numerator \( y + 1 \geq 0 \Rightarrow y \geq -1 \).

📌 The denominator \( y - 1 > 0 \Rightarrow y > 1 \), or \( y - 1 < 0 \Rightarrow y < 1 \).

📌 Case 1: \( y > 1 \), both numerator and denominator positive.

📌 Case 2: \( -1 \leq y < 1 \), numerator non-negative, denominator negative → expression negative, not allowed.

📌 Case 3: \( y < -1 \), numerator and denominator both negative → positive.

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