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When differentiability is defined for functions, are the endpoints of an interval included? In other words, in the definition "A function is differentiable in an interval (a,b) if it is differentiable at all points in the interval", does the interval have to be open? If not, how do we define differentiability at the endpoints?

Thank you for any replies.

LFC
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  • see https://math.stackexchange.com/questions/1295181/can-a-function-be-differentiable-at-the-end-points-of-its-closed-interval-doma and the linked post. cheers – l4teLearner Oct 30 '22 at 23:03
  • Additionally to linked above one dimensional case I would like recommend to read about continuation of a uniformly continuous function and partial derivative on the boundary of a domain in the case of several variables. – zkutch Oct 30 '22 at 23:07
  • Does this help? – Accelerator Oct 31 '22 at 04:10

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