What is the extreme f(x)=x^2+y^2-6xy+3x+6y-2 ?

The extreme f(x)=x^2+y^2-6xy+3x+6y-2 is Saddle(21/16 , 15/16)

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extreme f(x)=x^2+y^2-6xy+3x+6y-2

extreme

Saddle (\frac{21}{16}, \frac{15}{16})

Solution steps

Find the critical points:

(\frac{21}{16}, \frac{15}{16})

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

D (x, y) = - 32

Check the sign of at each critical point

Check critical point

(\frac{21}{16}, \frac{15}{16}) :

Saddle

Saddle (\frac{21}{16}, \frac{15}{16})

What is the extreme f(x)=x^2+y^2-6xy+3x+6y-2 ?
The extreme f(x)=x^2+y^2-6xy+3x+6y-2 is Saddle(21/16 , 15/16)