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Jonathan M. Borwein1, Xianfu Wang August 13, 1999 ABSTRACT. We prove a \typi al" subdi erentiability prin iple and apply it to a variety of omplete metri spa es of ontinuous fun tions on separable Bana h spa es; so as to obtain existen e of fun tions with maximal subdi erentials when ordered by in lusion. The relationship between ontinuous fun tions with maximal subdi erentials and nowhere monotone fun tions is dis ussed.