00:01
We're given a function f of x and it's x to the fourth minus 18x squared.
00:08
We want to find the intervals where f is increasing and decreasing.
00:12
So the first thing i'm going to do is take the derivative and that's 4x cubed minus 36x.
00:19
I'm going to find critical points by setting that derivative equal to zero and i'm going to take out a 4x.
00:27
That is going to leave me with x squared minus 9 so i can factor my difference of squares and i've got critical points at 0, negative 3, and 3.
00:47
Now i want to find some test points to plug in.
00:52
I'm going to put that first derivative into my calculator, get ready to test those points.
00:59
Okay so if i test something smaller than negative 3 like negative 4, i'm going to get out a negative.
01:12
If i test something between negative 3 and 0 like negative 2, i get out a positive.
01:20
1 gives me a negative and 4 gives me a positive.
01:27
So i know my graph is going to be decreasing, then increasing, then decreasing, then increasing.
01:36
So let's talk about those intervals.
01:40
I am going to be increasing from negative 3 to 0 and then from positive 3 to infinity.
01:51
I will be decreasing from negative infinity to negative 3 and then from 0 to positive 3.
02:04
Now i want relative extrema.
02:10
So i'm going to have a relative maximum, you can see that from my little shape of my graph, right here at 0, 0.
02:20
I have two relative minimums and i'm going to need to go and get the y coordinates for that.
02:31
And to get the y coordinates, you're going to need to go back to your original function to plug in.
02:37
So negative 3 gives me negative 81, 3 gives me negative 81.
02:43
So negative 3, negative 81, positive 3, negative 81...