Here is the task:

Find supremum and infimum of , if .

I have tried two ways:

1) searching for partial derivatives in order to find local extrema, but here is what happens:

So, it means that there is no local extreme points at all? Or all are extreme points?

2) from D follows that . Then I can get function and look for extreme points of g(x).

How do you think? Which way could fit? Or am I wrong in both of them?