find all locations and values of the local maximum and minima and the location of the saddle point of the given function f(x,y) =x^2 - 4xy +y^2 +12y + 2 Solution f(x,y) =x^2 - 4xy +y^2 +12y + 2 fx = 2x - 4y fy = -4x + 2y + 12 fxy = -4 fyx = -4 fxx = 2 fyy = 2 For saddle point, fx = fy = 0 2x - 4y = 0, thus x=2y -4x + 2y + 12 = 0 -8y + 2y + 12 = 0 y = 2, x=4 Possible point is (2,4)..

1. find all locations and values of the local maximum and minima and the location of the saddle
point of the given function
f(x,y) =x^2 - 4xy +y^2 +12y + 2
Solution
f(x,y) =x^2 - 4xy +y^2 +12y + 2
fx = 2x - 4y
fy = -4x + 2y + 12
fxy = -4
fyx = -4
fxx = 2
fyy = 2
For saddle point, fx = fy = 0
2x - 4y = 0, thus x=2y
-4x + 2y + 12 = 0
-8y + 2y + 12 = 0
y = 2, x=4
Possible point is (2,4).