Nature of the critical points of a function f(x y): local maximum/minimum/saddle and another ● 05
f(x, y) = ℯ^(-x² - y²) x y
fx(xy)= (-2 x² + 1) ℯ^(-(x² + y²)) y
fy(xy)= (-2 y² + 1) ℯ^(-(x² + y²)) x
fxy(xy)= (2x² - 1) (2y² - 1) ℯ^(-(x² + y²))
fyx(xy)= (2x² - 1) (2y² - 1) ℯ^(-(x² + y²))
fyy(xy)= 2y (2y² - 3) ℯ^(-(x² + y²)) x