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

The extreme x^2-y^2+4x+5y-4xy is Saddle(3/5 , 13/10)

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

extreme points

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

Saddle (\frac{3}{5}, \frac{13}{10})

Solution steps

Find the critical points:

(\frac{3}{5}, \frac{13}{10})

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

D (x, y) = - 20

Check the sign of at each critical point

Check critical point

(\frac{3}{5}, \frac{13}{10}) :

Saddle

Saddle (\frac{3}{5}, \frac{13}{10})

- \frac{x}{( x - 1 ) ( x - 3 ) ^{2}}

x^{2} - 4 x [- 1.4]

f (x) = - x^{4} + 2 x^{2} y - \frac{1}{2} y^{2} - 4 y + 12

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

f (x) = 2 x^{4} - 8 x

What is the extreme x^2-y^2+4x+5y-4xy ?
The extreme x^2-y^2+4x+5y-4xy is Saddle(3/5 , 13/10)