Taking the partial derivatives of and setting them to gives and .
Then my professor states that the critical points of are , and . Fine, I understand why, but I don't understand why the points , , , , and are not critical points.
How do you know that when you take , then you have to chose and not and ?
Because I know of an example ( ) which gives and . It still remains to solve for and (I see that and works for example. I've plotted the function and I saw 4 critical points (minimums), instead of 2 as my professor "would" find here.
So what am I overlooking?