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

The extreme f(x,y)=(xy(x^2-y^2))/(x^2+y^2) is None

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

extreme points

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

None

Solution steps

Find the critical points:

None

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

has no critical points, therefore there are no extreme points

None

f (x) = \frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16

f (x) = 3 + 81 x - 3 x^{3}

f (x, y) = 20 x y - x^{3} - 10 y^{2}

f (x) = - 5 (x - 4)^{4} + 2

f (x) = x^{2} - 5

What is the extreme f(x,y)=(xy(x^2-y^2))/(x^2+y^2) ?
The extreme f(x,y)=(xy(x^2-y^2))/(x^2+y^2) is None