Question

Consider the function f(x, y) = (2x - x^2)(2y - 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)

          Consider the function
f(x, y) = (2x - x^2)(2y - 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)

Consider the function
f(x, y) = (2x - x^2)(2y - y^2).
Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. fx =
fy =
fxx =
fxy =
fyy =
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)

Added by Susana W.

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