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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

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

Saddle

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

f (x) = x^{3} + 3 x^{2} + 9, 0 \leq x \leq 10

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

1.5 x^{2} + 45 x + 15000

- x^{3} + 300 x + y^{3} - 48 y + 9

f (x, y) = 8 x^{2} - 4 y^{2}

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