In this paper, we give a direct proof of Rockafellar's result that the subdifferential of a proper convex lower-semicontinuous function on a Banach space is maximal monotone. Our proof is simpler than those that have appeared to date. In fact, we show that Rockafellar's result can be embedded in a more general situation in which we can quantify the degree of failure of monotonicity in terms of a quotient like the one that appears in the definition of Frechet differentiability. Our analysis depends on the concepts of the least slope of a convex function, which is related to the steepest descent of optimization theory.