Precise descriptions of the thermodynamic properties of pure fluids require accurate vapor pressures and phase volumes as well as residual volumes, enthalpies and entropies. There is also the desirability of obtaining the density extrema in isothermal variations of the isochoric heat capacity, extrema of the isothermal compressibility and speed of sound, and densities where the reduced bulk modulus and isobaric expansivity are essentially independent of temperature (or have very weak maxima). While carefully fitted multiparameter equation of state models (EOS) show all of these qualities, cubic and other EOS based on 2- or 3-parameter corresponding states principles (CSP) usually do not, Tile common modifications to the attraction parameter and covolume dependence in generalized van der Waals models for improving vapor pressures and phase volumes do not improve descriptions of thew extrema for the derivative properties. This paper describes characteristics of the derivative propel-ties for methane from a highly accurate equation and compares them with results from several common EOS models. To obtain the extrema at all, the EOS covolume parameter must be at least temperature dependent, and most common models require density dependence. Accurate description is not, possible with such models unless the covolume has a complex dependence on both temperature and density.