Inflection Points

Core Sentence / 核心句

An inflection point is a point on the function where concavity actually changes.

中文理解：拐点不是“二阶导等于零的点”，而是函数凹凸性真正发生转换的定义域内点。

Candidate Test / 候选检查

Candidates often satisfy

$$f^{\prime \prime }(c)=0\text{or}{f}^{\prime \prime }(c)\text{ DNE}.$$

Then verify that $f^{\prime \prime }$ changes sign across $c$.

Watch Out / 易错点

• $f^{\prime \prime }(c)=0$ is not sufficient.
• even-multiplicity zeros may preserve the sign.
• the point must belong to the graph of $f$.

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 · Inflection Points

Connected Notes / 连接

• 微积分BC第6次正课-导数符号极值与凹凸性
• Concavity
• Second Derivative
• First Derivative Test