I've been watching the Khanacademy videos on Calculus and in this video, at 4:18: Spoiler: Khanacademy - Minima, maxima and critical points He talks about relative minima and maxima in an interval. He says that the relative extrema can't be at the endpoints. As far as I understand, in that case the interval would have to be an open one, but my question is what is the problem in having a closed interval and hence allowing them (to the relative extrema) to be at the endpoints? By having a closed interval: 1) I can ''define'' the absolute extrema in it, since we don't care about what is happening outside that interval. 2) The absolute extrema can be at the endpoints. Why do we care about what is happening outside an interval when finding relative extrema? Surely I'm misunderstanding something.