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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 f(x) = 15x + k(x - 1)(x - 2)(x - 3)(x - 4)

📌 But since $ f(x) $ is only cubic, the quartic term must vanish, so $ k = 0 $. Therefore:

📌 f(x) = 15x

📌 f(5) = 15 \cdot 5 = \boxed{75}

📌 Question: A cartographer is analyzing a terrain modeled by the function $ h(x) = x^3 - 3x^2 + 2x $, and wants to find the sum of all $ x $-coordinates where the terrain has horizontal slope.

📌 Solution: The slope of the terrain is given by the derivative:

📌 h'(x) = 3x^2 - 6x + 2

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