What is the extreme f(x,y)=x+y+1/x+4/y ?

The extreme f(x,y)=x+y+1/x+4/y is Minimum(1,2),Saddle(-1,2),Saddle(1,-2),Maximum(-1,-2)

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extreme f(x,y)=x+y+1/x+4/y

extreme points

f (x, y) = x + y + \frac{1}{x} + \frac{4}{y}

Minimum (1, 2), Saddle (- 1, 2), Saddle (1, - 2), Maximum (- 1, - 2)

Solution steps

Find the critical points:

(1, 2), (- 1, 2), (1, - 2), (- 1, - 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{8}{y ^{3}}

D (x, y) = \frac{16}{x ^{3} y ^{3}}

Check the sign of at each critical point

Check critical point

(1, 2) :

Minimum

Check critical point

(- 1, 2) :

Saddle

Check critical point

(1, - 2) :

Saddle

Check critical point

(- 1, - 2) :

Maximum

Minimum (1, 2), Saddle (- 1, 2), Saddle (1, - 2), Maximum (- 1, - 2)

3 x^{4} - 7 x^{2} + 6 x^{2} - 5 x - 8

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

P (x, y) = 200 x^{\frac{1}{2}} y^{\frac{1}{2}}

f (x) = \frac{x ^{2}}{9 - x ^{2}}

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

What is the extreme f(x,y)=x+y+1/x+4/y ?
The extreme f(x,y)=x+y+1/x+4/y is Minimum(1,2),Saddle(-1,2),Saddle(1,-2),Maximum(-1,-2)