Critical Point

Definition: Critical Point

Let $f:\mathcal{D}\subseteq {\mathbb{R}}^n\to \mathbb{R}$ be a Real Scalar Field.

We say that $f$ has a critical point at $\mathbf{a}\in \mathcal{D}$ if $f$ is not differentiable at $\mathbf{a}$ or its Gradient there is zero.

$$\nabla f(\mathbf{a})=\vec{0}$$