00:01
Alright, in your question, you're using the f function here, and you're interested in finding local or relative maximum.
00:09
Okay, so to do that, what we want to do is take our first derivative.
00:14
It's going to be negative 6x squared plus 18x plus 168.
00:23
We want to set our first derivative equal to zero.
00:28
And what i'm going to do is i'm going to, and we want to try to solve that, i'm going to factor out a gcf of negative.
00:34
6, which would give us x squared minus 3x minus 28.
00:47
Okay, so i just divided each of them by a negative 6.
00:50
Now i can factor the negative 6.
00:55
Let's just deal with the negative 6 gcf.
00:57
You're solving this equation, so you would divide both sides by negative 6, which makes it go away.
01:04
You're going to have x squared minus 3x minus 28 equals 0.
01:10
And to factor this, we want to factor it in two binomials.
01:14
We need two numbers that multiply to negative 28 that add to a negative 3.
01:20
So to do that, i'm just going to list my factors of negative 28.
01:24
It be 1 and negative 28.
01:29
2, negative 14.
01:32
3 won't go.
01:34
4 and negative 7.
01:36
Now, i'm going to stop there because 4 and negative 7 multiply to make the negative 2.
01:42
But they add to make the negative 3.
01:45
So that goes to x plus 4 and x minus 7 equals 0.
01:52
Then we set each factor equal to 0, and you come up with critical numbers, x equals negative 4 and x equals 7.
02:05
And again, that's what we call critical numbers...