00:01
So we're given this graph of the derivative of our function f of x, and we want to figure out where our function is increasing, decreasing, and then we're going to have to figure out where our local minimums and maximum values occur.
00:12
So for the first part, for part a, we'll figure out where we're increasing first.
00:17
So we're increasing wherever our derivative is positive.
00:22
So that's going to be from 0 to 1, and then from 5 to 7.
00:26
So we're increasing, increasing from 0 to 1 and from 5 to 7.
00:38
And we don't include 0, we don't include 1, we don't include 5, and we don't include 7, because we have a value of 0 at those points.
00:48
And that's 0, that's kind of an endpoint of our derivative, so we're not going to include that point either.
00:54
And now to figure out where we are decreased.
00:57
That is wherever our derivative is negative.
01:00
So if we look at our graph again, that's going to be from 1 to 5 and from 7 to 8.
01:07
So wherever our function, f prime of x in this case, wherever f prime of x is negative or wherever we have negative y values is going to be where we're decreasing.
01:18
So from 1 to 5 and from 7 to 8.
01:28
And now for part b, we want to find where our function has a local minimum and where they have local maximums.
01:35
So that's going to be where our derivative is equal to zero.
01:38
So the potential points will be here, here, and here...