What is the extreme f(x,y)=x^3+9y^4-20x^2y+2 ?

The extreme f(x,y)=x^3+9y^4-20x^2y+2 is Minimum(320000/243 ,(320000^2)/(1036800000))

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extreme f(x,y)=x^3+9y^4-20x^2y+2

extreme

Minimum (\frac{320000}{243}, \frac{32000 0 ^{2}}{1036800000})

Solution steps

Find the critical points:

(\frac{320000}{243}, \frac{32000 0 ^{2}}{1036800000})

\frac{\partial ^{2} f}{\partial x ^{2}} = 108 y^{2}

D (x, y) = 108 y^{2} (6 x - 40 y) - 1600 x^{2}

Check the sign of at each critical point

Check critical point

(\frac{320000}{243}, \frac{32000 0 ^{2}}{1036800000}) :

Minimum

Minimum (\frac{320000}{243}, \frac{32000 0 ^{2}}{1036800000})

What is the extreme f(x,y)=x^3+9y^4-20x^2y+2 ?
The extreme f(x,y)=x^3+9y^4-20x^2y+2 is Minimum(320000/243 ,(320000^2)/(1036800000))