What is the extreme x^2-5xy+4y^2-2x+5y ?

The extreme x^2-5xy+4y^2-2x+5y is Saddle(1,0)

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extreme x^2-5xy+4y^2-2x+5y

extreme points

x^{2} - 5 x y + 4 y^{2} - 2 x + 5 y

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = - 9

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

f (x) = x^{2} + 4 x + 11

f (x) = x^{2} + 4 x + 10

f (x) = x^{2} + 4 x + 17

f (x) = x 324 - x^{2}

y = - \frac{9}{4} x^{2} + 8

What is the extreme x^2-5xy+4y^2-2x+5y ?
The extreme x^2-5xy+4y^2-2x+5y is Saddle(1,0)