What is the extreme f(x,y)=x^2+xy+y^2-6y ?

The extreme f(x,y)=x^2+xy+y^2-6y is Minimum(-2,4)

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extreme f(x,y)=x^2+xy+y^2-6y

extreme points

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

Minimum (- 2, 4)

Solution steps

Find the critical points:

(- 2, 4)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- 2, 4) :

Minimum

Minimum (- 2, 4)

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

6 x^{5} - 10 x^{3}

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

f (x, y) = x^{3} + y^{3} - 36 x y

f (x) = \frac{x - 2}{x ^{3}}

What is the extreme f(x,y)=x^2+xy+y^2-6y ?
The extreme f(x,y)=x^2+xy+y^2-6y is Minimum(-2,4)