What is the extreme x^3-6xy+y^3 ?

The extreme x^3-6xy+y^3 is Saddle(0,0),Minimum(2,2)

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extreme x^3-6xy+y^3

extreme points

x^{3} - 6 x y + y^{3}

Saddle (0, 0), Minimum (2, 2)

Solution steps

Find the critical points:

(0, 0), (2, 2)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(2, 2) :

Minimum

Saddle (0, 0), Minimum (2, 2)

f (x) = \frac{5 - x}{2 x + 6}

f (x) = x - 3 x, - 1 \leq x \leq 6

f (x, y) = 5 x^{2} - 4 x y + 2 y^{2} - 36 x

f (x, y) = 37 - x^{2} - y^{2}

f (x) = 0.09 x^{2} + 16 x + 350, 0 < x < 150

What is the extreme x^3-6xy+y^3 ?
The extreme x^3-6xy+y^3 is Saddle(0,0),Minimum(2,2)