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

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

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

extreme points

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

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

f (x) = 2 x + 1 - \frac{18}{x}

f (x, y) = y - x

f (x, y) = 100 - x^{2} - y^{2}

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

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