What is the extreme 6x^2-2x^3+3y^2+6xy ?

The extreme 6x^2-2x^3+3y^2+6xy is Minimum(0,0),Saddle(1,-1)

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extreme 6x^2-2x^3+3y^2+6xy

extreme points

6 x^{2} - 2 x^{3} + 3 y^{2} + 6 x y

Minimum (0, 0), Saddle (1, - 1)

Solution steps

Find the critical points:

(0, 0), (1, - 1)

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

D (x, y) = - 72 x + 36

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(1, - 1) :

Saddle

Minimum (0, 0), Saddle (1, - 1)

What is the extreme 6x^2-2x^3+3y^2+6xy ?
The extreme 6x^2-2x^3+3y^2+6xy is Minimum(0,0),Saddle(1,-1)