What is the extreme x^3+8y^3-6xy+5 ?

The extreme x^3+8y^3-6xy+5 is Saddle(0,0),Minimum(1, 1/2)

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extreme x^3+8y^3-6xy+5

extreme points

x^{3} + 8 y^{3} - 6 x y + 5

Saddle (0, 0), Minimum (1, \frac{1}{2})

Solution steps

Find the critical points:

(0, 0), (1, \frac{1}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = 48 y

D (x, y) = 288 x y - 36

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(1, \frac{1}{2}) :

Minimum

Saddle (0, 0), Minimum (1, \frac{1}{2})

f (x) = 4 x^{3} - 60 x^{2} + 200 x

f (x) = x^{3} + 2 y^{2} + 3 x y + 8

f (x, y) = x^{2} + x y + y^{2} - 6 x - 9 y

\frac{x + 3}{x + 2}

f (x) = x (\frac{39900 - x}{5})

What is the extreme x^3+8y^3-6xy+5 ?
The extreme x^3+8y^3-6xy+5 is Saddle(0,0),Minimum(1, 1/2)