Relative Extremum

analysis

Definition

Relative Extremum

A function $f:D\to \mathbb{R}$ has a local extremum at $x_0\in D$ if $x_0$ is either a relative minima or a relative maxima of $f$.

Root Point

Let $f:D\to \mathbb{R}$ a differentiable function and $x_0$ be a relative extremum in the interior of $D$. Then:

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