The value set of a scalar field \(f:D\subseteq {\mathbb R}^n \to {\mathbb R}\) lies in \({\mathbb R}\) . This makes it possible to distinguish the values of a scalar field by size and to investigate whether local or global extreme values are assumed. Fortunately, this search for extremal points and extrema can be treated analogously to the one-dimensional case: Candidates are determined as the roots of the gradient (the counterpart of the first derivative) and then checked with the Hessian matrix (the counterpart of the second derivative) to see if the candidates are indeed extremal points. When searching for global extrema, the boundary of the domain of f must also be taken into account.