Question

Consider the function f(x, y) = e^{-2x-x^2-10y-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} = 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)

          Consider the function
f(x, y) = e^{-2x-x^2-10y-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} =
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)

Consider the function
f(x, y) = e^-2x-x^2-10y-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 =
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)

Added by Hector L.

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