Title: On types of degenerate critical points of real polynomial functions,
Abstract: In this paper, we consider the problem of identifying the type (local
minimizer, maximizer or saddle point) of a given isolated real critical point
$c$, which is degenerate, of a multivariate polynomial function $f$. To this
end, we introduce the definition of faithful radius of $c$ by means of the
curve of tangency of $f$. We show that the type of $c$ can be determined by the
global extrema of $f$ over the Euclidean ball centered at $c$ with a faithful
radius.We propose algorithms to compute a faithful radius of $c$ and determine
its type.