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

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

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extreme f(x,y)=y^3-3xy

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y

D (x, y) = - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = 10 x^{2} - 4 x y + 25 y^{2}

f (x) = \frac{- 3 x ^{2} y + 9 x y ^{2} - 12 x y}{x y}

f (x) = - 3 + 8 x - x^{3}

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

f (x, y) = 7 x^{2} - 10 y^{2}