What is the extreme xy+1/x+1/y ?

The extreme xy+1/x+1/y is Minimum(1,1)

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extreme xy+1/x+1/y

extreme points

x y + \frac{1}{x} + \frac{1}{y}

Minimum (1, 1)

Solution steps

Find the critical points:

(1, 1)

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

D (x, y) = \frac{4}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(1, 1) :

Minimum

Minimum (1, 1)

f (x) = x^{3} - 12 x^{2} + 45 x

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

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

f (x) = t 4 - t

x^{2} + \frac{1}{x}