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Apr 8, 2019 at 18:15 comment added Toby Bartels This example makes it clear that the issue is not that the first derivative might fail to exist (except at the point in question), so that it can't possibly have its own derivative. In this case, the first derivative exists everywhere and is even continuous, just not differentiable at zero.
May 7, 2014 at 0:18 vote accept Mike Shulman
May 6, 2014 at 22:26 history answered Michal R. Przybylek CC BY-SA 3.0