And once again, I'm not doing a proof of the extreme value theorem, but just to make you familiar with it and why it's stated the way it is. And just you could draw a bunch of functions here that are continuous over this closed interval. Here, our maximum point happens right when we hit b, and our minimum point happens at a. For a flat function, we could put any point as a maximum or the minimum point, and we'll see that this would actually be true. But let's dig a little bit deeper as to why f needs to be continuous and why this needs to be a closed interval. So first, let's think about why does f need to be continuous. Well, I could easily construct a function that is not continuous over a closed interval where it is hard to articulate a minimum or a maximum point.