What is the extreme g(x,y)=2x^2+3y^2-7 ?

The extreme g(x,y)=2x^2+3y^2-7 is Minimum(0,0)

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extreme g(x,y)=2x^2+3y^2-7

extreme points

g (x, y) = 2 x^{2} + 3 y^{2} - 7

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x, y) = x^{3} + 2 x y + y^{2} - 5 x

f (x) = x^{4} - 2 x^{2} - 3

f (x, y) = 25 - 5 x^{2} - y^{2}

f (x) = x^{3} + 3 x y^{2} - 15 x - 12 y

x^{3} - 6 x^{2} + 9 x + 1

What is the extreme g(x,y)=2x^2+3y^2-7 ?
The extreme g(x,y)=2x^2+3y^2-7 is Minimum(0,0)