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

The extreme f(x)=f(x,y)=-x^2-2y^2+xy+x+3y is Maximum(1,1)

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

extreme points

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

Maximum (1, 1)

Solution steps

Find the critical points:

(1, 1)

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

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(1, 1) :

Maximum

Maximum (1, 1)

f (y) = x^{3} + y^{3} - 27 x y

f (x) = - 2 x^{2} + 4 x + 6

f (x) = 12 x^{2} - 88 x + 121

f (x) = 9 x^{3} - 7 x^{2} + 3 x + 10, - 5 \leq x \leq 6

f (x, y) = 400 - 49 x^{2} - 9 y^{2}

What is the extreme f(x)=f(x,y)=-x^2-2y^2+xy+x+3y ?
The extreme f(x)=f(x,y)=-x^2-2y^2+xy+x+3y is Maximum(1,1)