00:01
In this problem, we will cover extrema of two variable functions.
00:05
So to find the critical points of this function f, we have to find the partial derivatives with respect to x and y, and set them equal to 0.
00:17
So we begin with the partial derivative with respect to x, and that's just taken the derivative holding y fixed.
00:25
So we get 3x squared plus 6y.
00:30
And just set that equal to 0.
00:35
We can rewrite this to say 6y equals negative 3x squared.
00:43
And we can further rewrite this to be y equals negative 1 half x squared.
00:50
So we'll keep that in mind for later.
00:54
So now we move on to the partial derivative of respect to y.
00:58
And that's just taking the derivative holding x fixed now.
01:02
So we have 6x plus 6y, and we set this equal to 0...