Kurs:Mathematik für Anwender (Osnabrück 2019-2020)/Teil I/Repetitorium/19/stetig nicht differenzierbar/Studentenfrage/Antwort

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I'm not sure what you mean with period. To me a period in mathematics is one of the following: w:en:Periodic_function or w:en:Period_(algebraic_geometry). I'm not sure how either is applicable here, but from context I assume you mean an interval.

Yes, a function can be continuous over an interval and at the same time not differentiable over the same interval .

Take for example
i.e. the absolute value function which was the topic of Aufgabe 10.3 and Aufgabe 14.3. It is continuous (you can use in the definition of continuity). You can show that it is not differentiable at by comparing difference quotients approaching from the left and from the right. From the left the differential would have to be -1 and from the right it would have to be 1.
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