  We prove a differential Harnack inequality for noncompact convex
hypersurfaces flowing with normal speed equal to a symmetric function of their
principal curvatures. This extends a result of Andrews for compact
hypersurfaces. We assume that the speed of motion is one-homogeneous, uniformly
elliptic, and suitably 'uniformly' inverse-concave as a function of the
principal curvatures. In addition, we assume the hypersurfaces satisfy
pointwise scaling-invariant gradient estimates for the second fundamental form.
For many natural flows all of these hypotheses are met by any ancient solution
which arises as a blow-up of a singularity.
