Using 773 muons found in hadronic events from 142 pb-1 of data at a c.m. energy of 57.8 GeV, we extract the cross section and forward-backward charge asymmetry for the e+e-→bb̄ process, and the heavy quark fragmentation function parameters for the Peterson model. For the analysis of the e+e-→bb̄ process, we use a method in which the behavior of the c quark and lighter quarks is assumed, with only that of the b quark left indeterminate. The cross section and asymmetry for e+e-→bb̄ are found to be Rb=0.57±0.06(stat)±0.08(syst) and Ab -0.59±0. 09±0.09, respectively. They are consistent with the standard model predictions. For the study of the fragmentation function we use the variable xE, the fraction of the beam energy carried by the heavy hadrons. We obtain xEc=0.56-0.05-0.03+0.04+0.03 and xEb=0.65-0.04-0.06+0.06+0.05, respectively. These are in good agreement with previously measured values.