  We consider the flow-equations for the 3 slow-roll parameters n_S (scalar
spectral index), r (tensor to scalar ratio), and dn_S/dlnk (running of the
spectral index). We show that the combination of these flow-equations with the
observational bounds from cosmic microwave background and large scale structure
allows one to put a lower bound on the fourth derivative of the inflationary
potential, M_P^4(V''''/V) > -0.02.
