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What is the main difference between the extreme points of a function of special types, such as: critical points, singular points, endpoints? Being more specific, I am talking about finding extreme values of derivatives, I understand the concept of critical points, which are where f'(x) = 0 and singular points, where f'(x) is not defined. But what about endpoint? Definition says that it is a point that do not belong to any open interval in D(f) which is kind of contradicting to the idea of finding endpoints

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    Their definitions are different and not in a subtle way, so could you be more specific?2011-12-05
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    I have edited the post2011-12-05
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    Hm. I don't see any contradiction: If my domain is $[a, b]$, then there is no open interval $I$ such that $a \in I \subset [a, b]$. So $a$ is an endpoint of the domain. What's bogus about this?2011-12-05
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    @DylanMoreland you say a is an endpoint of the domain, but why not b? Since the interval is a subset of [a, b]2011-12-06
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    $b$ is an endpoint as well, sure.2011-12-06

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