We review experimental results for the locus in the temperature-density plane of isothermal C-upsilon (constant volume heat capacity) extrema of Ar, Kr and Xe, and published Percus-Yevick and simulation equations of state. It is likely that the locus of C-upsilon maxima terminates at the critical point. We report new long (960 million Monte Carlo steps), 864 particle simulations of the heat capacity for the truncated Lennard-Jones potential (cutoff=2.5 sigma) near the liquid coexistence line, and establish directly that the locus of C-upsilon minima intersects the coexistence line. On the basis of calculations and simulations for model systems, we induce that previously reported C-upsilon extrema are caused by the interplay of three physical effects that we term, "aggregation," "caging," and "soft-core penetration." We test our hypothesis by carrying out calculations for a one-dimensional, nearest-neighbor, infinite-chain, truncated interaction model with the following potentials : Lennard-Jones, Lennard-Jones with hard core, Lennard-Jones with hard core and no soft repulsion, square well, and the inverse twelfth. Using our physical understanding, we successfully explain the qualitative changes in the behavior of the C-upsilon extrema as the interaction potential changes.