What is the extreme f(x,y)=y^3+9y^2-8xy+5x^2-2 ?

The extreme f(x,y)=y^3+9y^2-8xy+5x^2-2 is Minimum(0,0),Saddle(-232/75 ,-58/15)

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extreme f(x,y)=y^3+9y^2-8xy+5x^2-2

extreme points

f (x, y) = y^{3} + 9 y^{2} - 8 x y + 5 x^{2} - 2

Minimum (0, 0), Saddle (- \frac{232}{75}, - \frac{58}{15})

Solution steps

Find the critical points:

(0, 0), (- \frac{232}{75}, - \frac{58}{15})

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y + 18

D (x, y) = 60 y + 116

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(- \frac{232}{75}, - \frac{58}{15}) :

Saddle

Minimum (0, 0), Saddle (- \frac{232}{75}, - \frac{58}{15})

What is the extreme f(x,y)=y^3+9y^2-8xy+5x^2-2 ?
The extreme f(x,y)=y^3+9y^2-8xy+5x^2-2 is Minimum(0,0),Saddle(-232/75 ,-58/15)