  The appearance of the inflection point in the equation of state (EoS) is
associated with the second order phase transition. The high cumulants of
conserved quantities near the critical point are corresponding to the high
derivatives of the EoS near the inflection point. The critical behavior of high
cumulants of conserved charge near the QCD critical point, in particular, the
sign change, is closely related to the appearance of inflection point. We show
in general how the times of sign change of high cumulants relate to the order
of derivative. We also demonstrate that the character of inflection point of
EoS is as visible as the sign change of high cumulants in 3 systems, i.e., van
der Waals equation of fluid, magnetization of spin models and the baryon number
density of QCD matter. Therefore, we propose that the EoS, or the mean of
baryon number density, should be measured and studied together with its higher
cumulants in exploring QCD critical point in heavy ion collisions.
