00:01
Okay, suppose we have a rational inequality.
00:03
Rational means i have a denominator that i need to make sure i don't make it undefined.
00:08
And inequality means i have an inequality, so i'm considering different intervals that make this function positive or negative.
00:15
First thing i'm going to do is i'm going to look for my critical point, set the numerator and denominator equal to zero.
00:21
When i set the numerator equal to zero, i could set both terms equal to zero by the zero product property.
00:27
So x can be negative 1 or x can be positive 2.
00:31
And then setting my denominator equal to 0, i know that x can be negative 3.
00:37
So these are my three critical points.
00:39
Once i have my critical points, i can create intervals from these critical points that determine if my function will be positive or negative.
00:48
So intervals in between these critical points, i have three critical points.
00:54
So i'm going to have four intervals, starting from negative infinity to positive infinity.
00:58
On each interval, i need to pick a test point that i'm going to plug into my function.
01:05
When i plug my test point into my function, i'm ultimately determining if it's positive or negative.
01:12
Why do i care if it's positive or negative? well, because i want my function to be less than zero.
01:18
So really i want it to be below zero or negative.
01:21
Okay, to make this inequality true.
01:24
So i'm looking for the intervals there...