What is the extreme R(x,y)=x^2+5xy+6y^2+7x+17y+12 ?

The extreme R(x,y)=x^2+5xy+6y^2+7x+17y+12 is Saddle(-1,-1)

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extreme R(x,y)=x^2+5xy+6y^2+7x+17y+12

extreme points

R (x, y) = x^{2} + 5 x y + 6 y^{2} + 7 x + 17 y + 12

Saddle (- 1, - 1)

Solution steps

Find the critical points:

(- 1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 12

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 1, - 1) :

Saddle

Saddle (- 1, - 1)

f (x) = - 10 x^{2} + 1660 x - 49000

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

f (x) = 4 - (8 + 7 x)^{\frac{2}{7}}

\frac{3}{( x - 1 ) ( x ^{2} - 4 )}

f (x, y) = 2 x^{2} - 8 y^{2} - 4 x + 9 y + 2

What is the extreme R(x,y)=x^2+5xy+6y^2+7x+17y+12 ?
The extreme R(x,y)=x^2+5xy+6y^2+7x+17y+12 is Saddle(-1,-1)