00:01
Here, we're given a graph of a function, and we're asked to identify places where f has a local maximum or minimum.
00:08
So, a local max and min will happen if i zoom in, it looks like it has a global maximum.
00:15
So right here, if i were to just look at this region in here, that looks like it's a minimum.
00:25
And likewise, this point right here looks like it has a maximum.
00:29
And if i look at this point right here, it looks like it has a maximum as well.
00:33
Now you might be tempted to say that this one has a minimum as well, but it does not because at this point here, it doesn't actually reach that point.
00:44
And for the same reason, we don't have a local minimum here because it never actually reaches that point.
00:50
It's an open circle.
00:52
We also don't have a local minimum here because we have to approach it, and we don't approach it from anywhere.
00:58
So if we were to zoom in here, we wouldn't know if that was a max or a min.
01:03
So we have two local max.
01:06
So there's a local, let's say there's a local minimum at x equals, what is that? 1, 2, 3, 4, 5...