Consider the function
f(x,y) = (8x - x^2)(6y - 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_{xx} =
f_{xy} =
f_{yy} =
There are several critical points to be listed. List them lexicographically, 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)