The Lagrangian is

with partial derivatives (set equal to 0)





Case 1: If
, then

Then


So we have two critical points,
and 
Case 2: If
, then in the first equation we get

and from the third equation,

Then


but there are no real solutions for
, so this case yields no additional critical points.
So at the two critical points we've found, we get extreme values of
(min)
and
(max)