What is the extreme f(x)=x^3+y^2-6xy+6x+3y-2 ?

The extreme f(x)=x^3+y^2-6xy+6x+3y-2 is Minimum(5, 27/2),Saddle(1, 3/2)

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extreme f(x)=x^3+y^2-6xy+6x+3y-2

extreme

Minimum (5, \frac{27}{2}), Saddle (1, \frac{3}{2})

Solution steps

Find the critical points:

(5, \frac{27}{2}), (1, \frac{3}{2})

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

D (x, y) = 12 x - 36

Check the sign of at each critical point

Check critical point

(5, \frac{27}{2}) :

Minimum

Check critical point

(1, \frac{3}{2}) :

Saddle

Minimum (5, \frac{27}{2}), Saddle (1, \frac{3}{2})

What is the extreme f(x)=x^3+y^2-6xy+6x+3y-2 ?
The extreme f(x)=x^3+y^2-6xy+6x+3y-2 is Minimum(5, 27/2),Saddle(1, 3/2)