What is the extreme f(x,y)=x^3+8x^2y^2-8y^3-x+y ?

The extreme f(x,y)=x^3+8x^2y^2-8y^3-x+y is

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extreme f(x,y)=x^3+8x^2y^2-8y^3-x+y

extreme points

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

Minimum (\frac{- 0.27092 \dots + 12.07340 \dots}{6}, - 0.13012 \dots), Saddle (\frac{- 1.16242 \dots + 13.35124 \dots}{6}, 0.26953 \dots), Saddle (\frac{- 0.20866 \dots - 12.04354 \dots}{6}, - 0.11420 \dots)

Solution steps

Find the critical points:

(\frac{- 0.27092 \dots + 12.07340 \dots}{6}, - 0.13012 \dots), (\frac{- 1.16242 \dots + 13.35124 \dots}{6}, 0.26953 \dots), (\frac{- 0.20866 \dots - 12.04354 \dots}{6}, - 0.11420 \dots)

\frac{\partial ^{2} f}{\partial x ^{2}} = 16 x^{2} - 48 y

D (x, y) = 96 x^{3} - 768 x^{2} y^{2} - 288 x y - 768 y^{3}

Check the sign of at each critical point

Check critical point

(\frac{- 0.27092 \dots + 12.07340 \dots}{6}, - 0.13012 \dots) :

Minimum

Check critical point

(\frac{- 1.16242 \dots + 13.35124 \dots}{6}, 0.26953 \dots) :

Saddle

Check critical point

(\frac{- 0.20866 \dots - 12.04354 \dots}{6}, - 0.11420 \dots) :

Saddle

Minimum (\frac{- 0.27092 \dots + 12.07340 \dots}{6}, - 0.13012 \dots), Saddle (\frac{- 1.16242 \dots + 13.35124 \dots}{6}, 0.26953 \dots), Saddle (\frac{- 0.20866 \dots - 12.04354 \dots}{6}, - 0.11420 \dots)

f (t) = 4 t^{3} - 36 t^{2} + 10, t \geq 0

f (x) = 3 x^{4} + 20 x^{3} - 36 x^{2} - 4

2 x^{3} - 30 x^{2}, - 1 \leq x \leq 11

f (x) = x (1 - x)^{\frac{2}{5}}

f (x) = x^{2} - 2 x + 2, - 2 \leq x \leq 2

What is the extreme f(x,y)=x^3+8x^2y^2-8y^3-x+y ?
The extreme f(x,y)=x^3+8x^2y^2-8y^3-x+y is