What is the extreme f(x,y)= y/x+x^2y+6x ?

The extreme f(x,y)= y/x+x^2y+6x is Saddle(-1,2)

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extreme f(x,y)= y/x+x^2y+6x

extreme

Saddle (- 1, 2)

Solution steps

Find the critical points:

(- 1, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 4 x^{2} + \frac{4}{x} - \frac{1}{x ^{4}}

Check the sign of at each critical point

Check critical point

(- 1, 2) :

Saddle

Saddle (- 1, 2)

What is the extreme f(x,y)= y/x+x^2y+6x ?
The extreme f(x,y)= y/x+x^2y+6x is Saddle(-1,2)