Inflection Point

analysis

Definition

Inflection Point

Let $f:D\to \mathbb{R}$ be a differentiable function. A point $x_0\in D$ is called inflection point if $f^{\prime }$ has a relative extremum in $x_0$.

Let $f:D\to \mathbb{R}$ be a three-times differentiable function and $x_0\in D$. If:

$$f^{\prime \prime }(x_0)=0\wedge f^{\prime \prime \prime }(x_0)\ne 0$$

then $f$ has an inflection point at point $x_0$.