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

The extreme f(x,y)=x^2+3xy+y^2+5x-7y is Saddle(31/5 ,-29/5)

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extreme f(x,y)=x^2+3xy+y^2+5x-7y

extreme points

f (x, y) = x^{2} + 3 x y + y^{2} + 5 x - 7 y

Saddle (\frac{31}{5}, - \frac{29}{5})

Solution steps

Find the critical points:

(\frac{31}{5}, - \frac{29}{5})

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(\frac{31}{5}, - \frac{29}{5}) :

Saddle

Saddle (\frac{31}{5}, - \frac{29}{5})

f (x) = (x - 1)^{2} (x - 2) (x - 3)^{3}

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

f (x) = 2 x^{3} + x y^{2} + 5 x^{2} + y^{2} + 4

2 cos (3 x) + 2 sin (1 0^{\circ}) y + 3 x - 10 y = 0

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

What is the extreme f(x,y)=x^2+3xy+y^2+5x-7y ?
The extreme f(x,y)=x^2+3xy+y^2+5x-7y is Saddle(31/5 ,-29/5)