  We compute the complete post-Newtonian limit of the Palatini form of f(R)
gravities using a scalar-tensor representation. By comparing the predictions of
these theories with laboratory and solar system experiments, we find a set of
inequalities that any lagrangian f(R) must satisfy. The constraints imposed by
those inequalities allow us to find explicit functions that bound from above
and from below the possible nonlinear terms of the lagrangian. We conclude that
the lagrangian f(R) must be almost linear in R and that nonlinear corrections
that grow at low curvatures are incompatible with observations. This result
shows that modifications of gravity at very low cosmic densities cannot be
responsible for the observed cosmic speed-up.
