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

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

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

extreme points

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

Saddle (2, 1)

Solution steps

Find the critical points:

(2, 1)

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

D (x, y) = - 5

Check the sign of at each critical point

Check critical point

(2, 1) :

Saddle

Saddle (2, 1)

y = \frac{1}{2} x^{2} + (\frac{14 - 3 x}{4})^{2}

93000 x - 36000

f (x) = x^{4} - 32 x^{2} - 10

f (x, y) = x - 5 y

f (x) = x^{4} (x - 5) + 4

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