What is the extreme f(x,y)=xy+x^2+y^2+x-y+17 ?

The extreme f(x,y)=xy+x^2+y^2+x-y+17 is Minimum(-1,1)

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extreme f(x,y)=xy+x^2+y^2+x-y+17

extreme points

f (x, y) = x y + x^{2} + y^{2} + x - y + 17

Minimum (- 1, 1)

Solution steps

Find the critical points:

(- 1, 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Minimum

Minimum (- 1, 1)

f (x) = 4 x - 7 x^{\frac{4}{7}}

f (x) = 25 x - 25 x e^{- y} - 50 y - x^{2}

f (x, y) = x^{2} + x y - 10 x + y^{2} - 11 y + 37

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

f (x) = (x - 4) (x + 1) (x + 5)

What is the extreme f(x,y)=xy+x^2+y^2+x-y+17 ?
The extreme f(x,y)=xy+x^2+y^2+x-y+17 is Minimum(-1,1)