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

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

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

extreme points

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

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 8

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = 2 x^{3} + 24 x^{2} + 72 x

f (x, y) = 2 x^{3} - 3 x^{2} + 2 y^{3} - 6 y^{2}

f (x, y) = (x + 1, y - 1)

f (x, y) = x y - y

f (x, y) = x y + x

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