What is the extreme f(x,y)=x^3-15xy+y^3 ?

The extreme f(x,y)=x^3-15xy+y^3 is Saddle(0,0),Minimum(5,5)

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extreme f(x,y)=x^3-15xy+y^3

extreme points

f (x, y) = x^{3} - 15 x y + y^{3}

Saddle (0, 0), Minimum (5, 5)

Solution steps

Find the critical points:

(0, 0), (5, 5)

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

D (x, y) = 36 x y - 225

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(5, 5) :

Minimum

Saddle (0, 0), Minimum (5, 5)

f (x) = x^{3} - 5 x^{2} - 8 x + 3

f (x) = 2 x^{2} + 3 y^{2} - 4 x - 12 y + 13

f (x) = 5 - 6 x^{2} - 2 x^{3}

\frac{3}{2} x^{2} + x^{3} + 3 y^{2}

f (x) = \frac{3}{x}

What is the extreme f(x,y)=x^3-15xy+y^3 ?
The extreme f(x,y)=x^3-15xy+y^3 is Saddle(0,0),Minimum(5,5)