Using molecular-dynamics simulations and integral equations (Rogers-Young, Percus-Yevick, and hypernetted chain closures) we investigate the thermodynamics of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, D, has a maximum at a density rho(max) and a minimum at a density rho(min) < rho(max). In the pressure-temperature phase diagram the line of extrema in diffusivity is outside of the TMD line. Although this interparticle potential lacks directionality, this is the same behavior observed in simple point charge/extended water.