  The present paper is devoted to possible generalizations of the classic
Lagrange Mean Value Theorem. We consider a real-valued function of several
variables that is only assumed to be continuous. The main concept is to replace
the notion of the derivative by the so called bisequential tangent cone. We
first prove Rolle and Lagrange type results and then we turn to comparing this
cone with the Clarke subdifferential in the case of a Lipschitz function. We
also investigate an approach using normal cones.
