Finding the Maximum and Minimum Points on Graphs - Video Tutorials & Practice Problems

Finding Maximum and Minimum on a Graph

Alright, so now we're gonna do a quick recap on how to find the maximum point on a graph and how to find the minimum point on a graph. So here on this example of, I've got this kind of upside down you. Um So how do we find the maximum or minimum point? So what you'll see is that not all graphs have a maximum or a minimum? Um It's only when they kind of turn around like this, right where they're going up up, up, up up and then they turn around and start going down, right, so when we want to find the maximum point, it's that point where it turns around. So if you notice here the graph seems to be rising, rising, rising, rising, rising, rising, rising. And then on this side it's falling. Falling, falling. Right, so we gotta find that point where it turns around, so notice here it's still rising a little bit, right, it's still rising a little bit and then here it's pretty clear is the point where it turns around, I'm gonna do it in a different color there. So right here is the point where it turns around we're not doing any math here, I just want to be able to identify the maximum and the minimum. So right here that is our maximum. Okay, you're gonna wanna be able to do this um and find maximums and minimums on a graph. So what you'll notice is this one doesn't have a minimum. Um It went up up up to a point and then started going down down, down there wasn't a point where it was adam max bottom or max top, you might think this is a minimum here, this is a minimum here. Um but usually these graphs are gonna continue, so it would continue going down and it would be, you know, there wouldn't really be a minimum. So in this, when we see a critical point, it's kind of where it's turning around, they're not where it just stops, right? So that will be our critical point for our maximum. Um that we might want to identify, let's do the same thing with a minimum point right here. So I'm thinking you guys can guess where the minimum point is gonna be. Um But let's go ahead and do the same kind of method here. You see that the graph is falling and falling and falling right, and then on the other side it starts rising again. So there had to be a point where it turned around, it was falling for a while then now it's rising, where did it turn around? It's right here, that is our minimum point. And for now, all we wanna do is be able to recognize when a graph has a minimum or a maximum and then later on, we will be able to use this information when we're analyzing graphs. Cool, alright, let's move on