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v_1 & v_2 & v_3 \\ - DevRocket

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 At $ u = \pm rac{\sqrt{6}}{4} $:

📌 g = 3\left(rac{6}{16}

📌 ight) - 4\left(rac{36}{256}

📌 ight) = rac{18}{16} - rac{144}{256} = rac{9}{8} - rac{9}{16} = rac{18 - 9}{16} = rac{9}{16} = 0.5625

📌 So maximum of $ \sin 3x \sin x $ is $ rac{9}{16} $, thus minimum of $ f(x) = 1 - rac{9}{16} = rac{7}{16} $? But wait â this contradicts earlier thought.

📌 But where: $ f(x) = 1 - \sin 3x \sin x $, so minimum of $ f $ is when $ \sin 3x \sin x $ is **maximized**, which is $ rac{9}{16} $, so:

📌 f_{\min} = 1 - rac{9}{16} = rac{7}{16}

📌 But earlier we saw $ f(x) = 1 - rac{1}{2}(\cos 2x - \cos 4x) $. Letâs test $ x = rac{\pi}{2} $:

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