  We investigate the possibility to explain theoretically the galaxy rotation
curves by a gravitational potential in total absence of dark matter. To this
aim an analytic fourth-order theory of gravity, nonminimally coupled with a
massive scalar field is considered. Specifically, the interaction term is given
by an analytic function $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is
the scalar field. The gravitational potential is generated by a point-like
source and compared with the so called Sanders's potential that can be exactly
reproduced in this case. This result means that the problem of dark matter in
spiral galaxies could be fully addressed by revising general relativity at
galactic scales and requiring further gravitational degrees of freedom instead
of new material components that have not been found out up to now.
