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Home » \(racddx[3x^4] = 12x^3\), - AMAZONAWS

\(racddx[3x^4] = 12x^3\), - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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Solution: Since the difference $ f(x+1) - f(x) $ is linear, $ f(x) $ m...
f(x+1) = a(x+1)^2 + b(x+1) + c = a(x^2 + 2x + 1) + b(x + 1) + c = ax^2...
f(x+1) - f(x) = (ax^2 + 2ax + a + bx + b + c) - (ax^2 + bx + c) = 2ax...
f(x+1) - f(x) = 6x + 4
2a = 6 \Rightarrow a = 3, \quad a + b = 4 \Rightarrow 3 + b = 4 \Right...
Thus, the leading coefficient of $ f(x) $ is $ \boxed{3} $.
Question: A function $ f: \mathbb{R} \to \mathbb{R} $ satisfies $ f(a...
Solution: Let’s plug in $ a = b = 1 $ into the functional equation:
f(2) + f(0) = 2f(1) + 2f(1) = 4
We are given $ f(1) = 1 $, so:

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