00:01
In this question, we want to find all the local maxes, local mins, and saddle points of the function f of x, y, which is x squared plus xy plus 3x plus 2y minus 4.
00:13
I'm going to start by finding my critical points.
00:16
I need my partial of f with respect to x and my partial of f with respect to y.
00:21
So my partial of f with respect to x, it's 2x plus y plus 3, and i want to set this equal to 0.
00:30
Well, i also need my partial of f with respect to y.
00:35
That's going to be x plus 2.
00:39
It's just going to be x plus 2 this time, and i need both of these to be equal to 0.
00:47
So i'll start with the second equation.
00:50
That's the easier one.
00:51
I'm getting x equals negative 2.
00:54
I'm going to plug that in to my first equation.
00:58
2 times negative 2 is negative 4, plus y plus 3 is equal to 0.
01:04
Now negative 4 plus 3 is negative 1, so negative 1 plus y equals 0, so that i'm getting y equals 1...