 Hello, and welcome to a screencast about finding local and global extrema. Right, let's talk about a couple of the words here first. So extrema, remember that just means either where the graph has a maximum or a minimum. And then the local idea, that's just kind of if you look at the graph in a little area. So kind of like a neighborhood, I think of that. From algebra, you may have also heard the word relative, maximum or minimum. So relative and local are basically the same idea. And then global, that just means like overall. So a word you might have heard from algebra from before is absolute, maximums or minimums. Okay, so just know all these words mean the same thing and just be able to distinguish between them. Okay, so as we're looking at the graph, the graph is increasing here. And then it kind of hits a peak right up here. So if we were to kind of take a neighborhood around that peak, hopefully you agree that this point right here is definitely the highest point of that peak, didn't want that to happen. All right, try that again. There we go. That's the highest point of that peak. So this is a local maximum. Because as you look at points around that point, that's definitely the highest of all of them. Okay, now your graph starts decreasing and it decreases. And it does something kind of funky here, but it's still decreasing. Okay, until it gets to about down in here. So again, if we take a little snapshot around that point, you can tell down here is going to be the lowest point in that little neighborhood. So that would be considered a local minimum. Okay, now your graph starts to increase. And then it kind of settles down, but it's still increasing. So there's really no neighborhood in this area that we could take. Like if we were to look at this neighborhood here, well, this one might kind of be the biggest point. But then if you were to extend the neighborhood, like to here, then this one would be the highest point. Okay, so can you kind of see what I'm doing? So it's not like there really is a good neighborhood in this area, because the graph is constantly increasing and kind of settles down. But then again, there's not really any sort of smallest or biggest point in there. Okay, so that continues on until we hit this peak area up here. So again, if we were to take a little neighborhood around that, that peak there would give us a local maximum. Because again, it's the tallest in that area, the largest in that area. And then again, we're decreasing till we get down here to another valley. So let's say this point in here looks to be my local minimum. And I'm just using eyeballs since we don't have a function to work with. You just got to kind of guesstimate where it's going to be at. And then you don't even have to do this little neighborhood idea. I just like to do that, so it kind of gives you a smaller snapshot. So if you were to think about zooming in on that graph, that would be the highest or the lowest point of that area. Okay, so that takes care of our local extrema. Now, what about our global extrema? So is there a point on this graph that is the absolute tallest, the absolute highest, has the absolute biggest y value, whatever way you want to look at that? And yes, absolutely. This local max right here is actually also a global maximum, because that is the highest point on this graph. Okay, how about minimums? Is there a lowest point on this graph? Is there a point that the graph does not go below? And yes, again, as it turns out, it is at this local minimum. So this local minimum is also a global minimum. Now, that's not always going to be the case with the graphs, because this part of the graph continued on. I may go off the screen a little bit here. But if it were to go on, let's say down here, then this point down there, oops, there goes my menu again. This point down here at the bottom would have ended up being my global minimum. Okay, so I don't want you to necessarily think that because it's a local, it can be a global, or it only can be a global if it's a local or whatever. It just really depends on what the graph is doing. But because this graph happened to be cut off and this red area that I added on was not really there, as it turns out, the local and the global are actually the same thing for these two particular high and low points. Okay, thank you for watching.