What is the extreme f(x,y)=x^3+y^3-21xy ?

The extreme f(x,y)=x^3+y^3-21xy is Saddle(0,0),Minimum(7,7)

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extreme f(x,y)=x^3+y^3-21xy

extreme points

f (x, y) = x^{3} + y^{3} - 21 x y

Saddle (0, 0), Minimum (7, 7)

Solution steps

Find the critical points:

(0, 0), (7, 7)

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

D (x, y) = 36 x y - 441

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(7, 7) :

Minimum

Saddle (0, 0), Minimum (7, 7)

f (x) = - 3 x + ln (x)

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 1

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

f (x) = x + e^{- 4 x}

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

What is the extreme f(x,y)=x^3+y^3-21xy ?
The extreme f(x,y)=x^3+y^3-21xy is Saddle(0,0),Minimum(7,7)