00:01
Okay, so this is 9 plus x squared and then this is square root of 4 plus 12 minus x squared.
00:16
So, that's the distance and we're gonna take the derivative of that.
00:25
Before we do that, let's clean this up.
00:37
Just like that.
00:39
So, this becomes x squared minus 24x plus 148.
00:54
Okay, now let's take the derivative of this with respect to x.
01:00
2x over 2 times 9 plus x squared plus 2x minus 24 over x squared minus 24x plus 148.
01:18
Set it to zero.
01:20
This cancels out.
01:23
And, so what we're gonna do is we're gonna bring it, one of them to the other side.
01:32
And, we're gonna square both sides.
01:48
And, when you do that, you will get x squared over 9 plus x squared is equal to 4x squared minus 96x plus 576 over x squared minus 24x plus 148.
02:11
And, we're gonna solve this cross multiply.
02:15
So, we have x to the fourth minus 24x cubed plus 148x squared is equal to.
02:27
So, we get 4x to the fourth minus 96x cubed plus 184x squared minus 864x plus 1332.
02:47
Hopefully, we can reduce some stuff.
02:52
So, 3x to the fourth...