Consider the function Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. $f_x =$
$f_y =$
$f_{xx} =$
$f_{xy} =$
$f_{yy} =$
There are several critical points to be listed. List them lexicograhically, that is in ascending order by x-coordinates, and for equal x-coordinates in ascending order by y-coordinates (e.g., (1,1), (2, -1), (2, 3) is a correct order) The critical point with the smallest x-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest x-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest x-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest x-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

The critical point with the next smallest x-coordinate is
( , ) Classification: (local minimum, local maximum, saddle point, cannot be determined)

Your overall score for this problem is