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

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

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

extreme points

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

Saddle (- \frac{1}{2}, 1)

Solution steps

Find the critical points:

(- \frac{1}{2}, 1)

\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

(- \frac{1}{2}, 1) :

Saddle

Saddle (- \frac{1}{2}, 1)

K (r, s) = 6 r - s

f (x) = 7 x^{5} + 3 x^{3} - 2 x^{2} + x - 8

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

f (x, y) = 2 x^{2} + y^{2} + 8 x - 6 y + 20

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

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