What is the FUNCTION_MANY#extreme f(x,y)=x^3+y^2-6x^2+y-1 ?

The FUNCTION_MANY#extreme f(x,y)=x^3+y^2-6x^2+y-1 is Saddle(0,-1/2),Minimum(4,-1/2)

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FUNCTION_MANY#extreme f(x,y)=x^3+y^2-6x^2+y-1

extreme

Saddle (0, - \frac{1}{2}), Minimum (4, - \frac{1}{2})

Solution steps

Find the critical points:

(0, - \frac{1}{2}), (4, - \frac{1}{2})

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

D (x, y) = 2 (6 x - 12)

Check the sign of at each critical point

Check critical point

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

Saddle

Check critical point

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

Minimum

Saddle (0, - \frac{1}{2}), Minimum (4, - \frac{1}{2})

What is the FUNCTION_MANY#extreme f(x,y)=x^3+y^2-6x^2+y-1 ?
The FUNCTION_MANY#extreme f(x,y)=x^3+y^2-6x^2+y-1 is Saddle(0,-1/2),Minimum(4,-1/2)