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Home » Discover the Sharpest Adjectives Starting with H—Boost Your Vocabulary Instantly! - Abbey Badges

Discover the Sharpest Adjectives Starting with H—Boost Your Vocabulary Instantly! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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

📌 Set $ h'(x) = 0 $ to find where the slope is horizontal:

📌 3x^2 - 6x + 2 = 0

📌 Solve using the quadratic formula:

📌 x = \frac{6 \pm \sqrt{(-6)^2 - 4 \cdot 3 \cdot 2}}{2 \cdot 3} = \frac{6 \pm \sqrt{36 - 24}}{6} = \frac{6 \pm \sqrt{12}}{6} = \frac{6 \pm 2\sqrt{3}}{6} = 1 \pm \frac{\sqrt{3}}{3}

📌 The sum of the roots is:

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