Alright, so now we're going to 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 in this example, I've got this kind of upside-down U, so how do we find the maximum or minimum point? So what you'll see is that not all graphs have a maximum or minimum. 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've got to 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 it's the point where it turns around. I'm going to 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 going to want to be able to do this, and find maximums and minimums on a graph. So what you'll notice is this one doesn't have a minimum. It went up up up to a point and then started going down down down. There wasn't a point where it was at a max bottom or max top. You might think this is a minimum here, this is a minimum here, but usually, these graphs are going to continue. So it would continue going down and it would be, you know, there wouldn't really be a minimum. So, in this case, when we see a critical point, it's kind of where it's turning around there, not where it just stops. Right? So that will be our critical point for our maximum, 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 going to be, 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 want to 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.
1. Reading and Understanding Graphs
Finding the Maximum and Minimum Points on Graphs