00:01
For this problem, we are asked to find the absolute maximum and minimum values for the function f of xy equals xy on the rectangle defined by x between negative 1 and positive 1 and y between negative 1 and positive 1.
00:12
To begin, we want to take the partial derivative with respect to x, in which case we find a value of y, and then the partial derivative of f with respect to y, which gives x.
00:25
So we'll have a critical point at the point 0 .0.
00:28
In which case we can easily tell that we have a value of 0 at the point 0.
00:36
Now, that is one candidate point for absolute max or min, but we still need to figure out if there are any maximum or minimum values along the boundaries.
00:48
So i'll label the boundaries or the sides as 1, 2, 3, and 4.
00:55
So along side 1, let's see here...