What is the extreme f(x,y)=x^2-y^2+6xy+4x-8y+2 ?

The extreme f(x,y)=x^2-y^2+6xy+4x-8y+2 is Saddle(1,-1)

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extreme f(x,y)=x^2-y^2+6xy+4x-8y+2

extreme points

f (x, y) = x^{2} - y^{2} + 6 x y + 4 x - 8 y + 2

Saddle (1, - 1)

Solution steps

Find the critical points:

(1, - 1)

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

D (x, y) = - 40

Check the sign of at each critical point

Check critical point

(1, - 1) :

Saddle

Saddle (1, - 1)

f (x, y) = x y^{2} + 12 x^{3} y - x y

f (x) = \frac{2 x - 4}{x - 1}

f (x, y) = ln (e^{x} + e^{y})

y = x^{2} - 4 x - 5

x^{3} - 6 x^{2} + 9 x + 9

What is the extreme f(x,y)=x^2-y^2+6xy+4x-8y+2 ?
The extreme f(x,y)=x^2-y^2+6xy+4x-8y+2 is Saddle(1,-1)