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Home » Compute \( f'(u) \): -

Compute \( f'(u) \): -

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 This is an identity — true for all $ u $. But we must check if no restrictions apply. Since both sides are equal for all real $ u $, every value satisfies the equation.

📌 However, in the context of a math olympiad, if such an identity occurs, it implies the equation is trivial — but since its asking what is the value of $ u $, and no restriction is given, but the average equals $ 4u+2 $ for all $ u $, then any $ u $ works — but likely a unique solution is expected.

📌 Wait — rechecking: identity $ 4u + 2 = 4u + 2 $ is always true, so either infinitely many solutions or we missed a constraint.

📌 But in context, maybe $ u $ is a positive number, but not unique.

📌 But in olympiad problems, such equivalence usually means the equation is identically satisfied — so any $ u $ is acceptable, but if we assume a specific value is expected, perhaps a misstep.

📌 Subtract $ 4u $: $ 2 = 2 $ — always true.

📌 But to match format, likely meant to have a unique solution — re-express.

📌 $ 3u - 2 + 5u + 1 + 4u + 7 = (3+5+4)u + (-2+1+7) = 12u + 6 $ — correct.

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