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

The extreme f(x,y)=xln(x^2+y^2) is Saddle(0,1),Saddle(0,-1)

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extreme f(x,y)=xln(x^2+y^2)

extreme

Saddle (0, 1), Saddle (0, - 1)

Solution steps

Find the critical points:

(0, 1), (0, - 1)

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

D (x, y) = \frac{4 ( x + y ) ( x - y )}{( x ^{2} + y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Check critical point

(0, - 1) :

Saddle

Saddle (0, 1), Saddle (0, - 1)

What is the extreme f(x,y)=xln(x^2+y^2) ?
The extreme f(x,y)=xln(x^2+y^2) is Saddle(0,1),Saddle(0,-1)