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

The extreme f(x,y)=x^2+xy^2-2y is Saddle(-1/(\sqrt[3]{2)},-\sqrt[3]{2})

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

extreme points

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

Solution steps

Find the critical points:

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

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

Check the sign of at each critical point

Check critical point

Saddle

f (t) = e^{a t}

f (x) = x^{5} - 5 x^{3} - 20 x - 2

f (x) = 3 x^{4} - 8 x^{3} + 6 x^{2}

f (x) = x^{3} - 6 x^{2} + 9 x - 8

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

What is the extreme f(x,y)=x^2+xy^2-2y ?
The extreme f(x,y)=x^2+xy^2-2y is Saddle(-1/(\sqrt[3]{2)},-\sqrt[3]{2})