  In this Letter by utilizing the Noether symmetry approach in cosmology, we
attempt to find the tachyon potential via the application of this kind of
symmetry to a flat Friedmann-Robertson-Walker (FRW) metric. We reduce the
system of equations to simpler ones and obtain the general class of the
tachyon's potential function and $f(R)$ functions. We have found that the
Noether symmetric model results in a power law $f(R)$ and an inverse fourth
power potential for the tachyonic field. Further we investigate numerically the
cosmological evolution of our model and show explicitly the behavior of the
equation of state crossing the cosmological constant boundary.
