In the mean value theorems, we discuss the continuity of a given function in the closed interval and the differentiability in the open interval. Why we don’t discuss its differentiability in the closed interval?

Mean value theorem

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ajmaljoyia

In the mean value theorems, we discuss the continuity of a given function in the closed interval and the differentiability in the open interval. Why we don’t discuss its differentiability in the closed interval?

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