  The Noether symmetry of a generic $f(R)$ cosmological model is investigated
by utilizing the behavior of the corresponding Lagrangian under the
infinitesimal generators of the desired symmetry. We explicitly calculate the
form of $f(R)$ for which such symmetries exist. It is shown that the resulting
form of $f(R)$ yields a power law expansion for the cosmological scale factor.
We also obtain the effective equation of state parameter for the corresponding
cosmology and show that our model can provide a gravitational alternative to
the quintessence.
