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

The extreme f(x,y)=x^2+xy+y^2-y is Minimum(-1/3 , 2/3)

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

extreme points

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

Minimum (- \frac{1}{3}, \frac{2}{3})

Solution steps

Find the critical points:

(- \frac{1}{3}, \frac{2}{3})

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- \frac{1}{3}, \frac{2}{3}) :

Minimum

Minimum (- \frac{1}{3}, \frac{2}{3})

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

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

f (x) = x - 1

\frac{x - 7}{x ^{2}}

What is the extreme f(x,y)=x^2+xy+y^2-y ?
The extreme f(x,y)=x^2+xy+y^2-y is Minimum(-1/3 , 2/3)