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

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

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

extreme points

f (x, y) = 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)

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

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

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

- x^{3} - 3 x^{2}

f (x) = 2 x - 4 sin (x), 0 \leq x \leq 2 π

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