  Let T be Takagi's continuous but nowhere-differentiable function. Using a
representation in terms of Rademacher series due to N. Kono, we give a complete
characterization of those points where T has a left-sided, right-sided, or
two-sided infinite derivative. This characterization is illustrated by several
examples. A consequence of the main result is that the sets of points where
T'(x) is infinite have Hausdorff dimension one. As a byproduct of the method of
proof, some exact results concerning the modulus of continuity of T are also
obtained.
