  We consider the classical problem of maximizing the derivative at a fixed
point over the set of all bounded analytic functions in the unit disk with
prescribed critical points. We show that the extremal function is essentially
unique and always an indestructible Blaschke product. This result extends the
Nehari--Schwarz Lemma and leads to a new class of Blaschke products called
maximal Blaschke products. We establish a number of properties of maximal
Blaschke products, which indicate that maximal Blaschke products constitute an
appropriate infinite generalization of the class of finite Blaschke products.
