What is the extreme f(x,y)=x+y+(81)/(xy) ?

The extreme f(x,y)=x+y+(81)/(xy) is Minimum(3\sqrt[3]{3},3\sqrt[3]{3})

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extreme f(x,y)=x+y+(81)/(xy)

extreme points

f (x, y) = x + y + \frac{81}{x y}

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{162}{x y ^{3}}

D (x, y) = \frac{19683}{x ^{4} y ^{4}}

Check the sign of at each critical point

Check critical point

Minimum

f (x) = 2 (y + 1)^{2} + y^{2} - 2 y - 2

f (x) = x e^{\frac{x}{2}}, - 3 \leq x \leq 1

x + y - x y

p (x) = 3 x^{4} + 2 x^{3} + 5 x^{2} + a x - 2

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

What is the extreme f(x,y)=x+y+(81)/(xy) ?
The extreme f(x,y)=x+y+(81)/(xy) is Minimum(3\sqrt[3]{3},3\sqrt[3]{3})