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

The extreme f(x,y)=2x^2+3xy-3y^2+5x-5y+4 is Saddle(-5/11 ,-35/33)

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

extreme points

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

Saddle (- \frac{5}{11}, - \frac{35}{33})

Solution steps

Find the critical points:

(- \frac{5}{11}, - \frac{35}{33})

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

D (x, y) = - 33

Check the sign of at each critical point

Check critical point

(- \frac{5}{11}, - \frac{35}{33}) :

Saddle

Saddle (- \frac{5}{11}, - \frac{35}{33})

f (x) = 2 x - 6 sin (x)

f (x, y) = 2 x^{3} - 6 x y + y^{2} + 500

f (x) = 4 x e^{- x}, 0 \leq x \leq 2

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

f (x) = - x^{2} - 7 y^{2} + 9 x - 6 y + 2

What is the extreme f(x,y)=2x^2+3xy-3y^2+5x-5y+4 ?
The extreme f(x,y)=2x^2+3xy-3y^2+5x-5y+4 is Saddle(-5/11 ,-35/33)