Why do we talk about continuity of a function in closed interval and Differentiability of the same function in open interval ?
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Hi! Welcome to Math.SE. That is a good question and the answer is subtle. We do in fact talk about differentiability in closed intervals, but the results are not as good as when we restrict ourselves to open intervals. – Henrique Augusto Souza Sep 24 '18 at 05:14
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1Always be sure to search the website before posting a question. This answer (and question) might just be what you need: https://math.stackexchange.com/a/477736/266711 – Henrique Augusto Souza Sep 24 '18 at 05:15