What is the extreme f(x,y)=5x^2-3y^2+4xy-32x+10y ?

The extreme f(x,y)=5x^2-3y^2+4xy-32x+10y is Saddle(2,3)

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extreme f(x,y)=5x^2-3y^2+4xy-32x+10y

extreme points

f (x, y) = 5 x^{2} - 3 y^{2} + 4 x y - 32 x + 10 y

Saddle (2, 3)

Solution steps

Find the critical points:

(2, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6

D (x, y) = - 76

Check the sign of at each critical point

Check critical point

(2, 3) :

Saddle

Saddle (2, 3)

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

f (x) = 5 x + 5 sin (x)

f (x) = 5 - 3 sin (2 x)

\frac{2 x - 4}{3}

f (x, y) = 8 y^{2} + x^{2} - x^{2} y

What is the extreme f(x,y)=5x^2-3y^2+4xy-32x+10y ?
The extreme f(x,y)=5x^2-3y^2+4xy-32x+10y is Saddle(2,3)