What is the extreme f(x,y)=3x^2-5xy+6y^2+x-y ?

The extreme f(x,y)=3x^2-5xy+6y^2+x-y is Minimum(-7/47 , 1/47)

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extreme f(x,y)=3x^2-5xy+6y^2+x-y

extreme points

f (x, y) = 3 x^{2} - 5 x y + 6 y^{2} + x - y

Minimum (- \frac{7}{47}, \frac{1}{47})

Solution steps

Find the critical points:

(- \frac{7}{47}, \frac{1}{47})

\frac{\partial ^{2} f}{\partial x ^{2}} = 12

D (x, y) = 47

Check the sign of at each critical point

Check critical point

(- \frac{7}{47}, \frac{1}{47}) :

Minimum

Minimum (- \frac{7}{47}, \frac{1}{47})

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

f (x) = - 7 (2 x^{3} - \frac{125}{32})^{2} + 1

f (x) = \frac{( x y ) ^{2} + 8000 x + 8000 y}{x y}

f (x, y) = \frac{1}{( x + y )}

f (x) = \frac{1}{1 - x ^{2}}

What is the extreme f(x,y)=3x^2-5xy+6y^2+x-y ?
The extreme f(x,y)=3x^2-5xy+6y^2+x-y is Minimum(-7/47 , 1/47)