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

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

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

extreme points

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

None

Solution steps

Find the critical points:

None

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

has no critical points, therefore there are no extreme points

None

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

f (x, y) = x^{3} + y^{3} - 3 x^{2} - 6 y^{2} - 9 x

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

f (x) = x^{4} - 2 x^{2} + 3, - 2 \leq x \leq 3

f (x) = 3 cos (3 x), - \frac{π}{2} \leq x \leq \frac{π}{2}