00:01
Alright, this question asked me to find when this function f of x is greater than or equal to 7.
00:11
So, i'm just going to rewrite all this and set it greater than or equal to 7 and solve it.
00:25
Okay, when i have a problem like this, a polynomial greater than or less than something, i want that something to be zero.
00:33
So, i'm going to subtract a 7 from both sides of this inequality and i end up with 3x to the 3rd plus 4x squared minus 59x minus 20 is greater than or equal to zero.
00:52
Alright, the reason i want it equal to or greater than zero is because what i'm going to do is i'm going to graph it and i'm going to find where the graph is above or equal to the x -axis.
01:11
I want it to be greater than or equal to zero and that means above the x -axis and it will be including those points on the x -axis.
01:28
Okay, so when i graph this and i'm assuming that all y 'all have, you know, a pretty good knowledge of using your calculator, but i've graphed this from negative 10 to 10 and on my y's, i'm looking at it right now, i've got to make it a little bit larger.
01:59
I'm going to go from negative 10 to 100.
02:04
Actually, negative 100 to positive 100.
02:08
So, hold on just one second.
02:19
Okay, so i'm going from negative 10 to positive 10 and negative 100 to positive 100 and it looks like this.
02:31
Okay, so here's what i want.
02:38
I want the interval from this zero to this zero and it looks like it's going through the origin, but when i look at it a little bit better, i can tell that it's not.
02:53
It is not going through the origin.
02:55
It's a little bit on the negative side and then i want from this to infinity because i'm looking at the intervals where the graph is above the x -axis.
03:10
So, from here to here, the graph is above the x -axis and from here to infinity, it's above the x -axis.
03:21
So, i'm going to calculate these zeros and the way you do that is you push second trace, which is your calculate screen.
03:36
You push two, which says zero.
03:42
Then it asks you for a left bound.
03:44
If this is the point i'm looking for, this the farthest one to the left over here somewhere is to the left of it...