>Hi, Dr. Long.  I'm pretty much done with my homework,
>but had a question about some difficulty I had with
>14.  Bisection appears to be the best method in this
>case.  False Position wasn't too bad either.  But the
>Secant method went nuts on me.  Is there an easy way
>to explain why that happened in laymen's terms?  I
>tried to think it through graphically, but still
>couldn't get a hold on it.  It diverged very quickly
>away from any possible roots.  I appreciate any help.
>
    I can get secant to converge, if I'm careful to choose values of p0 and p1
    in the vicinity of the root. But with the choice given, secant is going to
    shoot us from one "branch" of the tangent function to another (one iterate
    is on one branch, while another is on another branch entirely!). I'm
    running it for 10000 iterations, to see if we get lucky, and get two
    iterates that are close together, but it doesn't look like it -- nope!
    So "Going nuts" is just flitting between branches of a periodic
    function....