What is the extreme f(x,y)=xy+3/x+9/y ?

The extreme f(x,y)=xy+3/x+9/y is Minimum(1,3)

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extreme f(x,y)=xy+3/x+9/y

extreme points

f (x, y) = x y + \frac{3}{x} + \frac{9}{y}

Minimum (1, 3)

Solution steps

Find the critical points:

(1, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{18}{y ^{3}}

D (x, y) = \frac{108}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Minimum (1, 3)

\frac{4 x}{x ^{2} - 9}

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 5 x + 2 y

2 x^{3} + 3 x^{2} - 180 x

sec^{2} (x)

x^{3} - 2 x^{2}

What is the extreme f(x,y)=xy+3/x+9/y ?
The extreme f(x,y)=xy+3/x+9/y is Minimum(1,3)