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May 16, 2014 at 16:56 comment added Dave L Renfro For more extreme examples, see my answer at How discontinuous can a derivative be?. Note that regarding the "levels of pathology" I list, each of #2, 4, 5, 6, 7 implies the differentiable function is nowhere monotone. (Recall that monotone in an interval implies at most countably many discontinuities in that interval.)
May 16, 2014 at 13:47 vote accept Ricky
May 16, 2014 at 13:37 history answered GH from MO CC BY-SA 3.0