Homework Soursea fxyx2xyy29x6y10 b fxy2x3xy25x2y2 c fxy3xyx2yxy2 d fxy x4
a. f(x,y)=(x^2)-xy+(y^2)+9x-6y+10
b. f(x,y)=2(x^3)+x(y^2)+5(x^2)+(y^2)
c. f(x,y)=3xy-(x^2)y-x(y^2)
d. f(x,y) = (x^4) + (y^4)-4xy+2
b. f(x,y)=2(x^3)+x(y^2)+5(x^2)+(y^2)
c. f(x,y)=3xy-(x^2)y-x(y^2)
d. f(x,y) = (x^4) + (y^4)-4xy+2
Solution
f(x,y)=(x^2)-xy+(y^2)+9x-6y+10 fx(x,y)=2x-y+9 fy(x,y)=-x+2y-6 fxx(x,y)=2 fyy(x,y)=2 fxy(x,y)=-1 so solving simultaneously for fx(x,y)=0 and fy(x,y)=0 x=-4 y=1 so D=fxx*fyy-fxy^2=3>0 fxx>0 so (-4,1) is a minima
