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) = - 28 x^{2} + 311 x

f (x, y) = x^{2} - 2 y^{2} - 5 x - 4 y + x y

f (x, y) = 5 - y ln (x)

f (x) = x^{2} + 4

f (x) = x^{2} - 7

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)