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

The extreme f(x,y)=x^2y+2xy-2xy^2+2 is Minimum(-2/3 , 1/3),Saddle(0,1)

Popular >

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

extreme points

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

Minimum (- \frac{2}{3}, \frac{1}{3}), Saddle (0, 1)

Solution steps

Find the critical points:

(- \frac{2}{3}, \frac{1}{3}), (0, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4 x

D (x, y) = 8 x y - 4 x^{2} - 8 x - 16 y^{2} + 16 y - 4

Check the sign of at each critical point

Check critical point

(- \frac{2}{3}, \frac{1}{3}) :

Minimum

Check critical point

(0, 1) :

Saddle

Minimum (- \frac{2}{3}, \frac{1}{3}), Saddle (0, 1)

f (x) = x^{4} + 4 x^{3} - 1

f (x, y) = x^{2} + x y + y^{2} - 31 y + 320

f (x, y) = 5 x + 3 y

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

f (x) = \frac{( x ^{2} - 7 x + 26 )}{x - 5}

What is the extreme f(x,y)=x^2y+2xy-2xy^2+2 ?
The extreme f(x,y)=x^2y+2xy-2xy^2+2 is Minimum(-2/3 , 1/3),Saddle(0,1)