.
Consider the function
f
(
x
,
y
)
=
(
2
x
−
x
2
)
(
6
y
−
y
2
)
.
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
x
x
=

f
x
y
=

f
y
y
=

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