Relative maxima and minima worked example

This is the Khan Academy exercise on relative maxima and minima, and they ask us to mark all the relative maximum points in the graph. Like always, pause this video and see if you can figure out which are the relative maximum points.

Okay, now let's work through this together. Just as a review, a relative maximum point is a point of the graph where the values of the graph around it are going to be less than or equal to the value of the graph at that point. So, for example, this point right over here would not be a relative maximum point because if we go to the right of it, the function is larger than at this point; it has a higher value than at this point.

This point over here, which looks like a peak of a mountain, and that's a pretty good giveaway. If it looks at the top of a hill or peak of a mountain, this looks like a really good candidate. If we move to the right a little bit, we get lower values for our function, and if we move to the left a little bit, we get lower values of our function. And so, this is a relative maximum point.

Let's do another example here. They say mark all the relative minimum points in the graph. Well, a relative minimum point is a point of the graph where, if we were to look at the values of the graph around it, they're all going to be the same or higher. One way to think about it, this would be the bottom of a dip in the graph, and you see one big dip in this graph, and the bottom of it is right over there. So, that would be a relative minimum point.

You can see if you have the x values around it, the values of the function at those x values are all going to be the same or higher than the value of the function right at this point. That's not true for any of the other points that we can see of this graph.