Consider the following plot:
Plot3D[RealAbs[(x-5)+y],{x,4.999,5.001},{y,0,0.001}]
The above plot has a white space where the derivative has a discontinuous jump (at $y=5$)
If instead I consider
Plot3D[Abs[(x-5)+y],{x,4.999,5.001},{y,0,0.001}]
The white space is gone.
I understand that, according this answer, I can get rid of the whitespace by using the Exclusions option.
However, I am wondering why one command produces the whitespace by default and the other doesn't?
(my naive guess would be that because Abs thinks the argument is complex, that mathematica doesn't detect an exclusion at the kink)
y, the difference presumably has to do with the automatic detection forExclusions.D[RealAbs[(x - 5) + y], y]evaluates; whereas,D[Abs[(x - 5) + y], y]is meaningless. Including the optionExclusions -> Nonewill eliminate the white line. – Bob Hanlon Feb 08 '20 at 20:43