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Home » \[ 48 = 2^4 \times 3^1 \] - Tacotoon

\[ 48 = 2^4 \times 3^1 \] - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The numerator must be zero:

📌 \[ 1 - t^2 = 0 \]

📌 \[ t^2 = 1 \]

📌 \[ t = \pm 1 \]

📌 Check the second derivative or evaluate \(C(t)\) at critical points and endpoints to confirm maximum:

📌 \[ C(1) = \frac{k \cdot 1}{1^2 + 1} = \frac{k}{2} \]

📌 \[ C(-1) = \frac{k \cdot (-1)}{(-1)^2 + 1} = \frac{-k}{2} \]

📌 Since \(C(t) \to 0\) as \(t \to \pm \infty\), the maximum occurs at \(t = 1\).

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