What is the extreme u(x,y)=(2-x)(y-1)+2(x-2)^2+2(y-1)^2-3 ?

The extreme u(x,y)=(2-x)(y-1)+2(x-2)^2+2(y-1)^2-3 is Minimum(2,1)

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extreme u(x,y)=(2-x)(y-1)+2(x-2)^2+2(y-1)^2-3

extreme

Minimum (2, 1)

Solution steps

Find the critical points:

(2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = 15

Check the sign of at each critical point

Check critical point

(2, 1) :

Minimum

Minimum (2, 1)

What is the extreme u(x,y)=(2-x)(y-1)+2(x-2)^2+2(y-1)^2-3 ?
The extreme u(x,y)=(2-x)(y-1)+2(x-2)^2+2(y-1)^2-3 is Minimum(2,1)