I am stuck with the following problem. I can find the absolute minimum or maximum of a function with 2 variables or more, but I can't prove that absolute values exist.
Assume we have the following function:
I need to show that the absolute maximum and minimum values exist
My idea: For a function to have absolute min/max value, the domain set should be compact: that is, closed and bounded and the function be continuous. But I am really stuck here. I dont know how to show that the domain set is compact. Could anyone please help me with this matter?