Absolute Extrema

Core Sentence / 核心句

Absolute extrema are the highest and lowest attained outputs on the entire domain or specified interval.

中文理解：绝对最大值和最小值必须与整个指定区间比较，不只是比附近点高或低。

Closed Interval Method / 闭区间方法

1. Find critical numbers inside $(a,b)$.
2. Add endpoints $a,b$.
3. Evaluate $f$ at every candidate.
4. Compare all outputs.

Watch Out / 易错点

• local maximum need not be the absolute maximum.
• endpoints may be absolute extrema without being interior critical numbers.
• include nondifferentiable domain points and piecewise joins when relevant.
• Extreme Value Theorem guarantees existence under its hypotheses but does not calculate the values.

Search and Source Mentions / 搜索与出现位置

Mentioned In / 出现位置

• 微积分BC第6次正课 · Absolute Extrema

Connected Notes / 连接

• 微积分BC第6次正课-导数符号极值与凹凸性
• Extreme Value Theorem
• First Derivative Test
• Derivatives