Posted by Adam Getchell on October 13, 2002 at 04:00:19:
In Reply to: you all are really making this too difficult... posted by T.Gracken on October 04, 2002 at 07:50:18:
: if you want the derivative for y=|x|, just use the (piece-wise) definition.
: that is
: 1. if x > 0 then |x| = x, so for y = |x|, when x > 0, y' = 1
: 2. if x < 0 then |x| = -x, so for y = |x|, when x < 0, y' = -1
: 3. if x = 0, the limit defining a derivative does not exist.
You just restated what I said.
And, your point 3 is incorrect. At x=0, you have a singularity which can be handled by analytic continuation into the complex plane. However, that would be calculus of residues, which is beyond the scope of this discussion.
Nice definitions can be found on Mathworld
Post a Followup