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

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

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

extreme points

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

Minimum (4, - 2)

Solution steps

Find the critical points:

(4, - 2)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(4, - 2) :

Minimum

Minimum (4, - 2)

f (x) = 40 x^{2} + \frac{600}{x}

(y^{2} - x^{2}) (y - 2)

U (x, y) = x y

f (x) = 7 - (7 + 5 x)^{\frac{2}{5}}

f (x) = \frac{x ^{5}}{5} - \frac{4 x ^{4}}{4} + 2

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