What is the extreme f(x,y)=10+x^2+2y^2 ?

The extreme f(x,y)=10+x^2+2y^2 is Minimum(0,0)

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extreme f(x,y)=10+x^2+2y^2

extreme points

f (x, y) = 10 + 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) = \frac{4 x ^{2}}{4 x - 8}

x^{4} - x^{3} - 3 x^{2} + 5 x - 2

2 x^{3} + 9 x y^{2} + 15 x^{2} + 27 y^{2}

f (x, y) = e^{x^{2} + y^{2} - 4 y}

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

What is the extreme f(x,y)=10+x^2+2y^2 ?
The extreme f(x,y)=10+x^2+2y^2 is Minimum(0,0)