Is there any algorithm to quickly determine "zero points" (i.e. points with undefined derivation) of absolute values functions which are nested multiple times? I do know, that any part of this piecewise function is going to be linear or constant (no exponential, trigonometry, logarithm, polynomial, rational, nothing more "difficult" than linear)
For example, given function such as this? $f(x) = |||||||x|-32|-16|-8|-4x|-2|+|||||x-33|-17|-9|-5|-3|-5|-2-14$
I need to find some general algorithm (usable in programming homework, where no graphing tools are available), these coefficients can vary. Any help is appreciated, I believe I'm fairly good at math, but this seems as unsolvable problem to me, so just pointing out into the right direction might really help.
Thanks a lot for any direction.