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 points

f (x, y) = \frac{y}{x} + x^{2} y + 6 x

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)

y = - \frac{3}{2 x + 2}

4 sin (x) + 5 cos (x)

f (x) = - 3 x^{2} + 24 x - 5

f (x) = x^{2} + y^{2} - 9

f (x \cdot y) = ln (2 x + 2 y)

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)