.
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?