What is the extreme (y^2-x^2)(y-2) ?

The extreme (y^2-x^2)(y-2) is Minimum(4/3 ,0),Saddle(0,0),Saddle(2,2),Saddle(2,-2)

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extreme (y^2-x^2)(y-2)

extreme

Minimum (\frac{4}{3}, 0), Saddle (0, 0), Saddle (2, 2), Saddle (2, - 2)

Solution steps

Find the critical points:

(\frac{4}{3}, 0), (0, 0), (2, 2), (2, - 2)

\frac{\partial ^{2} f}{\partial y ^{2}} = - 2 (y - 2)

D (y, x) = - 2 (6 y - 4) (y - 2) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(\frac{4}{3}, 0) :

Minimum

Check critical point

(0, 0) :

Saddle

Check critical point

(2, 2) :

Saddle

Check critical point

(2, - 2) :

Saddle

Minimum (\frac{4}{3}, 0), Saddle (0, 0), Saddle (2, 2), Saddle (2, - 2)

What is the extreme (y^2-x^2)(y-2) ?
The extreme (y^2-x^2)(y-2) is Minimum(4/3 ,0),Saddle(0,0),Saddle(2,2),Saddle(2,-2)