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)

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 (6 - 2 x)^{2}

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

f (x, y) = - 4 \cdot \frac{x ^{2} + 6 x + 8}{y ^{2} + 6 y + 6}

f (x) = x + \frac{108}{x ^{2}}

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)