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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Saddle

Check critical point

(1, - 1) :

Saddle

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

x^{3} - 48 x y + 64 y^{3}

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

f (x) = e^{x} - 7 e^{- x} - 8 x

e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

f (x) = x^{11} - 3 x^{9} + 2

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