00:02
Okay, so you are given f of x is equal to 5x minus 6 over x plus 5.
00:14
You want to find the critical points, so you want to find the derivative.
00:19
So f prime of x is, you're using the quotient rule.
00:29
So it is x plus 5 times 5 minus 5.
00:41
5x minus 6 over x plus 5 squared.
00:50
So that is 5x minus 5x and it's 25 plus 6, which is 31.
00:58
So this is 31 over x plus 5 squared to find the critical points.
01:05
You set it equal to 0.
01:06
Notice that this is never equal to 0, so there are no critical points.
01:13
Use interval notation to indicate whether the function is increasing or decreasing.
01:20
So we look at what is happening around, notice the domain, x cannot be equal to negative 5.
01:30
So we look what's happening around negative 5.
01:35
To the left of negative 5, it is positive, the derivative, and it is also positive.
01:44
So this function is always increasing.
01:48
So it is increasing from negative infinity to negative 5...