00:01
Okay, so you have fx is equal to 2x cubed over x minus 1.
00:12
So part 1, find the domain.
00:17
The domain, the denominator cannot be equal to 0.
00:20
So x cannot be equal to 1.
00:23
This will lead to a vertical asymptote.
00:29
So we will get there in just a second.
00:35
Find the x intercepts so the x intercepts are when y is equal to zero so you have 2x cubed over x minus 1 is equal to 0 so 2x cubed is equal to 0 and x is equal to 0 so x equal to 0 so x equal to 0 is equal to 0 so x equal to 0 is the x intercept find the y intercept.
01:11
The y intercept is when x is equal to zero.
01:18
If x is equal to zero, then y is equal to zero.
01:21
So that is also zero.
01:27
Find any horizontal asymptotes.
01:31
The degree of the numerator is greater than the degree of the denominator.
01:36
So this is c.
01:40
No horizontal.
01:43
Acentotes.
01:44
You also could do this with limits.
01:47
So there are no horizontal asymptotes.
01:54
Vertical acentotes, there is a vertical acentote where the domain doesn't exist.
02:00
So there is an asymptote at x equals 1.
02:05
I feel like there's some parts missing, so i'm going to fill in what i think should be there.
02:12
And that would be increasing, decreasing, and then maximums and minimums.
02:27
So you can take the derivative.
02:38
So f prime of x, it is the bottom times the derivative of the top.
02:53
Move this over, times the top.
03:02
The derivative at the bottom is one over the bottom squared.
03:10
And then you can find the critical values.
03:13
So set it equal to zero, so we don't care about that denominator...