What is the extreme f(x)=x^3+y^3-30xy ?

The extreme f(x)=x^3+y^3-30xy is Saddle(0,0),Minimum(10,10)

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extreme f(x)=x^3+y^3-30xy

extreme points

f (x) = x^{3} + y^{3} - 30 x y

Saddle (0, 0), Minimum (10, 10)

Solution steps

Find the critical points:

(0, 0), (10, 10)

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

D (x, y) = 36 x y - 900

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(10, 10) :

Minimum

Saddle (0, 0), Minimum (10, 10)

\frac{x ^{2} + 4 x + 3}{( x + 2 ) ^{2}}

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

f (x) = x^{4} - 72 x + 5

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

f (x, y) = (x - y) (2 x + y) (x + 1)

What is the extreme f(x)=x^3+y^3-30xy ?
The extreme f(x)=x^3+y^3-30xy is Saddle(0,0),Minimum(10,10)