monotonicity 相关的数学解题方法?

1. 📝 Identify: f(x) = 4x^3 - 5x^2 + 10x 2. 📐 Derivative: f'(x) = 12 * x ^ 2 + 10 - 10 * x

这道题的难度是多少?

🔵 Intermediate (Level 10/20)

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Increasing/Decreasing Intervals Find the intervals where f(x) = 4x³ - 5x² + 10x is increasing and decreasing. — Calculus — Detailed Solution | AhaStep

Home›数学›Increasing/Decreasing Intervals Find the intervals where f(x) = 4x³ - 5x² + 10x is increasing and decreasing. — Calculus

📐 数学难度 10 — 🔵 Intermediatemonotonicity👁 12 浏览次数⏱ 1 min read

Increasing/Decreasing Intervals Find the intervals where f(x) = 4x³ - 5x² + 10x is increasing and decreasing. — Calculus

📝 Problem

Find the intervals where f(x) = 4x³ - 5x² + 10x is increasing and decreasing.

✨详细解答

1. 📝 Identify: 4x^3 - 5x^2 +

2. 📐 Derivative: f'(

3. 🔍 Critical points: f'(x) ≠ 0 → monotone

4. 📊 Sign chart f'(x): f'(x) + trên (-∞; +∞)

🔒 4 步剩余

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1. 📝 Identify: 4x^3 - 5x^2 +

2. 📐 Derivative: f'(

3. 🔍 Critical points: f'(x) ≠ 0 → monotone

4. 📊 Sign chart f'(x): f'(x) + trên (-∞; +∞)

🔒 4 步剩余

Increasing/Decreasing Intervals Find the intervals where f(x) = 3x³ - 4x² + 1x is increasing and decreasing. — Calculus

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Solve Find the intervals where f(x) = 2x³ - 9x² + 9x is increasing and decreasing. — Step-by-Step Solution by AhaStep