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 points

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

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)

g (x) = x^{6} - 2 x^{5} + 8 x^{4}

y = \frac{1}{3} x e^{e x^{2}}

f (x) = \frac{x - 4}{x ^{2} - 9}

f (x, y) = x^{2} - 2 x + 6 y^{2} + 6

4 x + 6 y

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)