Theorem. Suppose that f is a function which is differentiable
on the open interval I. If either f '(x) > 0 or f '(x) < 0 for all x in I then f has an
inverse f^{ 1} which is
defined and is differentiable on f(I). That is, for each a in I, f^{ 1} is
differentiable at b = f(a) and

