What is the extreme f(x,y)=3xy+x^2y ?

The extreme f(x,y)=3xy+x^2y is Saddle(0,0),Saddle(-3,0)

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extreme f(x,y)=3xy+x^2y

extreme points

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

Saddle (0, 0), Saddle (- 3, 0)

Solution steps

Find the critical points:

(0, 0), (- 3, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 4 x^{2} - 12 x - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 3, 0) :

Saddle

Saddle (0, 0), Saddle (- 3, 0)

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

f (x) = x^{3} + y^{3} - 24 x y

f (x) = x^{4} - 50 x^{2} + 6

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

\frac{3 x ^{2}}{x ^{2} - 25}

What is the extreme f(x,y)=3xy+x^2y ?
The extreme f(x,y)=3xy+x^2y is Saddle(0,0),Saddle(-3,0)