What is the extreme f(x,y)=x^2(x+y)+6xy ?

The extreme f(x,y)=x^2(x+y)+6xy is Saddle(0,0),Saddle(-6,18)

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extreme f(x,y)=x^2(x+y)+6xy

extreme points

f (x, y) = x^{2} (x + y) + 6 x y

Saddle (0, 0), Saddle (- 6, 18)

Solution steps

Find the critical points:

(0, 0), (- 6, 18)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 4 x^{2} - 24 x - 36

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 6, 18) :

Saddle

Saddle (0, 0), Saddle (- 6, 18)

f (x) = - 4 x^{3} + 12 x^{2} - 10

f (x) = 2 x + 7 ln (x)

68 - 11

f (x) = x^{3} - 75 x + 3

y = (x - 5)^{2} - 4

What is the extreme f(x,y)=x^2(x+y)+6xy ?
The extreme f(x,y)=x^2(x+y)+6xy is Saddle(0,0),Saddle(-6,18)