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

The extreme f(x,y)=x^2+xy-5x-2y^2+2y is Saddle(2,1)

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

extreme points

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

Saddle (2, 1)

Solution steps

Find the critical points:

(2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = - 9

Check the sign of at each critical point

Check critical point

(2, 1) :

Saddle

Saddle (2, 1)

\frac{x + 2}{x ^{2} - 7 x - 18}

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

f (x, y) = 2 x^{3} + y^{2} - 4 x y + x^{2} - 24 x + 6 y + 7

\frac{1}{3} x^{3} - 12 x^{2} + 144 x + 2

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

What is the extreme f(x,y)=x^2+xy-5x-2y^2+2y ?
The extreme f(x,y)=x^2+xy-5x-2y^2+2y is Saddle(2,1)