00:01
All right, so we're going to use the first and second derivative test to find any local maxes or min.
00:04
So let's do go ahead and find the derivative first.
00:06
Finding this derivative, we get 6x minus 6x squared for the first derivative.
00:12
The second derivative is going to be 6 minus 12x.
00:17
So we need both.
00:17
We're going to use the first derivative test first, which says, hey, find your critical points and figure out what the behavior of the first derivative is before and after it's critical points.
00:25
That will tell you whatever max or min.
00:27
The first derivative test here is going to be the following.
00:30
Find the critical points.
00:31
With a function first derivative equals zero does not exist.
00:33
This is a polynomial, so it will exist everywhere, so just find out it equal zero.
00:37
And when you do that, you pull out it at 6x, and you'll get one minus, minus, two x, excuse me, one minus two x, just double check that that works.
00:47
Beautiful.
00:48
So then we get 6x equals zero and 1 minus 2x equals zero.
00:52
That means x equals zero is a critical point, and x equals one half is a critical point.
00:58
So there's your critical points that we have there.
01:01
Now what we're going to do is check the behavior of those critical points of the first, of the first derivative's behavior of those critical points to the left and right.
01:08
That will tell us we have a local max or min.
01:10
So plug in values of your first derivative to the left of zero.
01:13
A nice one would be negative 1.
01:14
So that's a negative times looks like one minus two times negative one...