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I am having a little trouble understanding one of the concepts presented in my calculus class. I do not understand how the endpoints of an open interval can be differentiable. My teacher says that the endpoints of a closed interval can not be differentiable because the limit can not be approached from the left side of the left endpoint and the right side of the right endpoint. This makes sense to me, even though some research shows that there is no consensus on this subject. What I do not understand is why this argument can not be applied to open intervals as well. Wouldn't the endpoint of an open interval being differentiable imply that the left endpoint can be approached from the left? I do not understand how that is possible? Can anyone explain this concept to me more effectively? Thanks in advance for any help.

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# Differentiability on an Open Interval

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