What is the extreme x^3+y^3-30xy ?

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

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extreme x^3+y^3-30xy

extreme points

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) = 1 - 9 x - 6 x^{2} - x^{3}

y = \frac{4 x ^{2}}{x ^{2} - 4}

f (x, y) = x^{3} + 3 x y^{2} - 3 y^{2} + 3 x^{2} + 11

f (x) = - \frac{10}{x ^{2} - 3 x + 14}

y = x^{2} + 3

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