00:01
Okay, in this problem, we have a two -dimensional function, f of x and y, that's sine of x squared, y, squared.
00:09
We're mostly interested in the point zero -zero the origin.
00:13
You want to figure out the behavior there.
00:17
So let's first of all verify as a critical point.
00:21
So we take the x derivative, we get 2x squared times the cosine of x squared y squared, and the y derivative gives us 2 y squared x times the cosine of x squared y squared.
00:31
Squared.
00:34
So clearly if x and y are both zero, then this is going to be zero.
00:39
I also want to point out that there's a whole lot, there are two whole lines of critical points along the x and y axis.
00:48
If i choose any point that has x equals zero, both of these are going to be zero.
00:54
And any point with y equals zero are also going to give both of these equal to zero.
01:00
So there's way more than just this critical point, but we're just going to be interested in this one...