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

The extreme f(x,y)=x^2-2xy+2y^2x is Saddle(0,1),Saddle(0,0),Minimum(1/4 , 1/2)

Popular >

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

extreme points

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

Saddle (0, 1), Saddle (0, 0), Minimum (\frac{1}{4}, \frac{1}{2})

Solution steps

Find the critical points:

(0, 1), (0, 0), (\frac{1}{4}, \frac{1}{2})

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

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

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Check critical point

(0, 0) :

Saddle

Check critical point

(\frac{1}{4}, \frac{1}{2}) :

Minimum

Saddle (0, 1), Saddle (0, 0), Minimum (\frac{1}{4}, \frac{1}{2})

f (x) = 56 - 18 x + 3 x^{2}

f (x) = 3 + 4 x^{2} - x^{4}

y = \frac{1}{3} x^{3} - \frac{5}{2} x^{2} + 6 x - 2

f (x, y) = x^{2} - 2 x y - 3 x + 6

f (x) = 6 + 12 x - 3 x^{2}

What is the extreme f(x,y)=x^2-2xy+2y^2x ?
The extreme f(x,y)=x^2-2xy+2y^2x is Saddle(0,1),Saddle(0,0),Minimum(1/4 , 1/2)