What is the extreme f(x,y)=x^2+7xy+y^2 ?

The extreme f(x,y)=x^2+7xy+y^2 is Saddle(0,0)

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extreme f(x,y)=x^2+7xy+y^2

extreme points

f (x, y) = x^{2} + 7 x y + y^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 45

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 2 x^{2} - 16 ln (x)

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

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

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

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

What is the extreme f(x,y)=x^2+7xy+y^2 ?
The extreme f(x,y)=x^2+7xy+y^2 is Saddle(0,0)