What is the extreme f(x,y)=(x-1)^2+y^3-3y^2-9y+5 ?

The extreme f(x,y)=(x-1)^2+y^3-3y^2-9y+5 is Minimum(1,3),Saddle(1,-1)

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extreme f(x,y)=(x-1)^2+y^3-3y^2-9y+5

extreme

Minimum (1, 3), Saddle (1, - 1)

Solution steps

Find the critical points:

(1, 3), (1, - 1)

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

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

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Check critical point

(1, - 1) :

Saddle

Minimum (1, 3), Saddle (1, - 1)

What is the extreme f(x,y)=(x-1)^2+y^3-3y^2-9y+5 ?
The extreme f(x,y)=(x-1)^2+y^3-3y^2-9y+5 is Minimum(1,3),Saddle(1,-1)