What is the extreme f(x,y)=x^2+5xy+y^2-2x+y-6 ?

The extreme f(x,y)=x^2+5xy+y^2-2x+y-6 is Saddle(-3/7 , 4/7)

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extreme f(x,y)=x^2+5xy+y^2-2x+y-6

extreme points

f (x, y) = x^{2} + 5 x y + y^{2} - 2 x + y - 6

Saddle (- \frac{3}{7}, \frac{4}{7})

Solution steps

Find the critical points:

(- \frac{3}{7}, \frac{4}{7})

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

D (x, y) = - 21

Check the sign of at each critical point

Check critical point

(- \frac{3}{7}, \frac{4}{7}) :

Saddle

Saddle (- \frac{3}{7}, \frac{4}{7})

f (x) = 2 x^{3} + 3 x^{2} - 9 x - 9

f (x) = \frac{1}{4} x^{4} - x, - 4 \leq x \leq 4

12

f (x) = (x^{2} + 10) (100 - x^{2})

21

What is the extreme f(x,y)=x^2+5xy+y^2-2x+y-6 ?
The extreme f(x,y)=x^2+5xy+y^2-2x+y-6 is Saddle(-3/7 , 4/7)