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

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

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

extreme points

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

Saddle (1, 1), Maximum (- 1, 1)

Solution steps

Find the critical points:

(1, 1), (- 1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 1

D (x, y) = - \frac{4}{x ^{3}}

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Check critical point

(- 1, 1) :

Maximum

Saddle (1, 1), Maximum (- 1, 1)

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