  We find analytical vacuum stability or bounded below conditions for general
scalar potentials of a few fields. After a brief review of copositivity we go
beyond it. We discuss the vacuum stability conditions of the general potential
of two real scalars, without and with the Higgs boson included in the
potential. As further examples, we give explicit vacuum stability conditions
for the two Higgs doublet model with no explicit CP breaking, and for the
$\mathbb{Z}_{3}$ scalar dark matter with an inert doublet and a complex
singlet. We give a short overview of positivity conditions for tensors of
quartic couplings via tensor eigenvalues. A Mathematica notebook with the
conditions is included with the source files.
