Gauvin and Tolle have obtained bounds on the direc t ional derivative limit quotient of the optima l value func t ion for mathematical programs containing a ri ght-hand side perturbation. In this paper , we extend the results of Gauvin and Tolle to the general mathematical program in w ' uich a parameter appears arbitraril y in the constraints and in the objective function. An imp licit function theorem is app lied to transform the general mathema t ical program to a locally equivalent inequality constrained program , and , under conditions used by Gauvin and Tolle , their upper and lower bounds on the optimal

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