It is nowadays accepted that the universe is undergoing a phase of
accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae
(SNeIa) and several LSS observations. Future SNeIa surveys and other probes
will make it possible to better characterize the dynamical state of the
universe renewing the interest in cosmography which allows a model independent
analysis of the distance - redshift relation. On the other hand, fourth order
theories of gravity, also referred to as f(R) gravity, have attracted a lot
of interest since they could be able to explain the accelerated expansion
without any dark energy. We show here how it is possible to relate the
cosmographic parameters (namely the deceleration q0​, the jerk j0​, the
snap s0​ and the lerk l0​ parameters) to the present day values of f(R)
and its derivatives f(n)(R)=dnf/dRn (with n=1,2,3) thus offering
a new tool to constrain such higher order models. Our analysis thus offers the
possibility to relate the model independent results coming from cosmography to
the theoretically motivated assumptions of f(R) cosmology.Comment: 18 pages, 4 figure