00:01
Consider this function of two variables, f of xy is equal to x cubed minus 2y.
00:07
We'd like to find the global extrema on this unit square.
00:12
So first of all, let's see if we have any critical numbers that are in our region.
00:21
So f of x, the first partial with respect to x is 3x squared.
00:28
And notice that this is equal to zero when x is equal to zero which is one of our boundary curves f y x y is negative two this is linear and we get no new points of interest okay so if we look at the lines x equals zero and x equals one so let's do zero first we have f of zero y that just gives us a linear again.
01:19
And so we have no new points of interest.
01:25
Okay, so let's look at y equals zero and y equals one.
01:36
Okay, so when y is equal to zero, we have f of x zero, which is now just a function of one variable, and that's equal to x cubed, right? and it just has a critical number at zero, right? so we have to check the point zero zero, which is one of our intersection points anyway...