The equality of unilateral derivates

C. J. Neugebauer has shown that if f is a continuous function of bounded variation defined on the real line, then the set E where the upper right derivate differs from the upper left derivate is of measure zero and first category. Here it is shown that this result is best possible; that is, given any measure zero first category set K, there is a continuous function of bounded variation for which $K \subseteq E$. It is also shown that if f is monotone, then E is $\sigma$-porous. This result can be used to provide an elementary proof of the fact that for an arbitrary function f the left and right essential cluster sets are identical except at a $\sigma$-porous set of points, a result first proved by L. Zajíček.