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

The extreme f(x,y)=(x-1)^2+2y^2 is Minimum(1,0)

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

extreme points

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

Minimum (1, 0)

Solution steps

Find the critical points:

(1, 0)

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

D (x, y) = 8

Check the sign of at each critical point

Check critical point

(1, 0) :

Minimum

Minimum (1, 0)

What is the extreme f(x,y)=(x-1)^2+2y^2 ?
The extreme f(x,y)=(x-1)^2+2y^2 is Minimum(1,0)