What is the extreme f(x,y)= 1/2 x^4-3xy+3y^4 ?

The extreme f(x,y)= 1/2 x^4-3xy+3y^4 is

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extreme f(x,y)= 1/2 x^4-3xy+3y^4

extreme points

f (x, y) = \frac{1}{2} x^{4} - 3 x y + 3 y^{4}

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = 36 y^{2}

D (x, y) = 216 x^{2} y^{2} - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

Minimum

Check critical point

Minimum

3 x^{2}

f (x) = x^{2} - 12 x + 10

f (x, y) = 2 x^{2} - 4 x + y^{2} - 4 y + 1

x^{4} - x^{3} + 2 x^{2} - 1

f (x) = \frac{1}{2} (3 x - 1), x \leq 3

What is the extreme f(x,y)= 1/2 x^4-3xy+3y^4 ?
The extreme f(x,y)= 1/2 x^4-3xy+3y^4 is