What sort of problems can occur when using newton's method to solve (x-1)^40 for the roots/zeros?
Near this root convergence will not be quadratic but linear (happens when
the derivative at the root is zero). Also as the power is high (40) not only
will the convergence be linear it will be slow, as close to the root, after an
itteration step will be (39/40) times the error before the step.
RonL