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

The extreme f(x,y)=xy^2+2xy is Saddle(0,0),Saddle(0,-2)

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

extreme points

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

Saddle (0, 0), Saddle (0, - 2)

Solution steps

Find the critical points:

(0, 0), (0, - 2)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(0, - 2) :

Saddle

Saddle (0, 0), Saddle (0, - 2)

e^{- 1.5 x^{2}}

f (x) = x^{3} - \frac{3}{2} x^{2}, - 5 \leq x \leq 6

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

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

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

What is the extreme f(x,y)=xy^2+2xy ?
The extreme f(x,y)=xy^2+2xy is Saddle(0,0),Saddle(0,-2)