What is the extreme 72y^2+x^2-x^2y ?

The extreme 72y^2+x^2-x^2y is Minimum(0,0),Saddle(1,12),Saddle(1,-12)

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extreme 72y^2+x^2-x^2y

extreme

Minimum (0, 0), Saddle (1, 12), Saddle (1, - 12)

Solution steps

Find the critical points:

(0, 0), (1, 12), (1, - 12)

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

D (y, x) = 144 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(1, 12) :

Saddle

Check critical point

(1, - 12) :

Saddle

Minimum (0, 0), Saddle (1, 12), Saddle (1, - 12)

What is the extreme 72y^2+x^2-x^2y ?
The extreme 72y^2+x^2-x^2y is Minimum(0,0),Saddle(1,12),Saddle(1,-12)