I have attempted to come up with functions that are continuous and differentiable on an arbitrary interval $(-1, 1)$, but their derivative is not continuous on $(-1,1)$, ideally due to a division by zero in the denominator. Perhaps it is due to the time, or my ignorance, but I am failing at arriving at an example. This is a recommended practice problem for an upcoming exam, just so I'm transparent.
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I think your textbook might have demonstrated such kind of examples. Make use of those. – xbh Dec 12 '18 at 06:54
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3https://math.stackexchange.com/questions/292275/discontinuous-derivative – T. Fo Dec 12 '18 at 06:55
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@xbh, if only that were the case. My textbook is probably the vaguest intro to analysis textbook ever written. Thank you for the reference T. Ford! If you want to link that as an answer, I'll mark it as accepted. – Joe Dec 12 '18 at 07:02
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OK, then. If you haven't seen such things, it would be pretty struggle for you to construct. – xbh Dec 12 '18 at 07:11