  We investigate equations of motion and future singularities of $f(R,T)$
gravity where $R$ is the Ricci scalar and $T$ is the trace of stress-energy
tensor. Future singularities for two kinds of equation of state (barotropic
perfect fluid and generalized form of equation of state) are studied. While no
future singularity is found for the first case, some kind of singularity is
found to be possible for the second. We also investigate $f(R,T)$ gravity by
the method of dynamical systems and obtain some fixed points. Finally, the
effect of the Noether symmetry on $f(R,T)$ is studied and the consistent form
of $f(R,T)$ function is found using the symmetry and the conserved charge.
