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Home » Case 1: Neither A nor B is selected - Imagemakers

Case 1: Neither A nor B is selected - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 C'(t) = rac{(3)(t^2 + 4) - (3t + 2)(2t)}{(t^2 + 4)^2}

📌 3(t^2 + 4) - 2t(3t + 2) = 3t^2 + 12 - (6t^2 + 4t) = -3t^2 - 4t + 12

📌 C'(t) = rac{-3t^2 - 4t + 12}{(t^2 + 4)^2}

📌 To find where $ C(t) $ is increasing, we solve:

📌 -3t^2 - 4t + 12 > 0

📌 This is a quadratic inequality. First, find the roots:

📌 -3t^2 - 4t + 12 = 0 \Rightarrow 3t^2 + 4t - 12 = 0

📌 t = rac{-4 \pm \sqrt{16 + 144}}{6} = rac{-4 \pm \sqrt{160}}{6} = rac{-4 \pm 4\sqrt{10}}{6} = rac{-2 \pm 2\sqrt{10}}{3}

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