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

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

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

extreme points

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)

\frac{x}{ln ( x ^{2} )}

x^{2 x}

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

f (x, y) = \frac{500}{( 4 + x ^{2} + y ^{2} )}

f (x) = \frac{5 + x}{4 - x}

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