00:01
Okay, so we want to find the maximum and minimum values of this f, subject to it being on this sphere.
00:09
So this is a lagrange multiplier problem.
00:13
Here's our objective function.
00:23
Lambda's our lagrange multiplier.
00:33
So let's take the derivatives.
01:32
And then we set each of those equal to zero.
02:26
Okay, so equation three tells us that lambda z equals phi.
02:35
That tells us that lambda is not zero and z is not zero, unless one of them's infinite, which seems completely unlikely and basically impossible.
02:47
So that means these both have to be non -zero.
02:51
So that means equation one tells us, since lambda is non -zero, that x equals zero, okay? and then equation two, i can factor like this.
03:26
That means that y equals zero or lambda is minus one.
03:33
Let's look at this.
03:35
So x equals zero.
03:36
If i take equation four, and so i've got two choices...