What is the extreme f(x)=98y^2+x^2-x^2y ?

The extreme f(x)=98y^2+x^2-x^2y is Minimum(0,0),Saddle(14,1),Saddle(-14,1)

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extreme f(x)=98y^2+x^2-x^2y

extreme points

f (x) = 98 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (14, 1), Saddle (- 14, 1)

Solution steps

Find the critical points:

(0, 0), (14, 1), (- 14, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 196

D (x, y) = 196 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(14, 1) :

Saddle

Check critical point

(- 14, 1) :

Saddle

Minimum (0, 0), Saddle (14, 1), Saddle (- 14, 1)

f (x) = \frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )}

f (x) = x y - 2 x - 2 y - x^{2} - y^{2}

f (x, y) = 2 x^{3} + x y^{2} + 5 x^{2} + y^{2} + 6

f (x) = x (6 - 2 x)^{2}

f (x, y) = 22 x^{4} + 22 y^{4} - 4 x y + 18

What is the extreme f(x)=98y^2+x^2-x^2y ?
The extreme f(x)=98y^2+x^2-x^2y is Minimum(0,0),Saddle(14,1),Saddle(-14,1)