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

The extreme f(x,y)=x^2y+xy^3 is None

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

extreme points

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

None

Solution steps

Find the critical points:

None

x^{2} y + x y^{3}

has no critical points, therefore there are no extreme points

None

3 x^{4} - x^{6}

f (x, y) = 6 x + 3 y - x^{3} - y^{3}

f (x) = \frac{( x ^{2} + x + 4 )}{( 3 + x ^{2} )}

(1 - x^{2})^{2}

f (x) = 3 + 9 x - 3 x^{2} - x^{3}