00:01
For this problem, we're looking at the relation between the graph of f prime of x and the graph of f of x.
00:07
And so the problem supposedly gives a graph, but it's not included.
00:11
So i just sketched this one out.
00:14
And we can talk about the basic principles using this.
00:19
So the first question is, where is f of x increasing? so f of x is increasing any time that f prime is greater than 0.
00:31
So i'm looking for places that are above the x -axis.
00:39
So this is above the x -axis.
00:42
And in this graph, that happens.
00:44
That should be an x, x -axis.
00:48
In this graph, that happens between 0 and 2.
00:57
And it also happens from 4 to infinity.
01:15
The next thing asks where it's decreasing.
01:18
And so decreasing is when our derivative is less than 0, which is going to be below the x -axis.
01:30
And so that happens from negative infinity to 0.
01:36
And i think this should be m's.
01:40
And also happens on 2 to 4.
01:46
And then we want to know if our local maxes are mins.
01:58
And so the easiest way to do this, i think, is to make a little sign chart.
02:03
It's a little bit easier to see than the graph, i think.
02:07
So if we call this f prime of x, we know we've got a 0 at 0.
02:12
We've got a 0 at 2 and a 0 at 4.
02:16
And so maxes and mins only happen where your first derivative is equal to 0.
02:21
So we want to check those places...