What is the extreme F(x,y)=12x^2+5xy-17x+7y-2y^2+5 ?

The extreme F(x,y)=12x^2+5xy-17x+7y-2y^2+5 is Saddle(3/11 , 23/11)

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extreme F(x,y)=12x^2+5xy-17x+7y-2y^2+5

extreme points

F (x, y) = 12 x^{2} + 5 x y - 17 x + 7 y - 2 y^{2} + 5

Saddle (\frac{3}{11}, \frac{23}{11})

Solution steps

Find the critical points:

(\frac{3}{11}, \frac{23}{11})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = - 121

Check the sign of at each critical point

Check critical point

(\frac{3}{11}, \frac{23}{11}) :

Saddle

Saddle (\frac{3}{11}, \frac{23}{11})

5 x y e^{- x^{2} - y^{2}}

f (x) = - 2 x^{2} - 8 x + 5

f (x) = t - t^{\frac{1}{3}}

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

f (x, y) = 3 x^{3} - 2 x^{2} y + 5 x y - y^{3} - 1

What is the extreme F(x,y)=12x^2+5xy-17x+7y-2y^2+5 ?
The extreme F(x,y)=12x^2+5xy-17x+7y-2y^2+5 is Saddle(3/11 , 23/11)