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

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

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extreme f(x)=xy+1/x+1/y

extreme points

f (x) = 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)

y = 3 x^{2} - 4 x, 0 \leq x \leq 3

f (x) = x^{5} - 5 x - 10

f (x) = 4 - \frac{16}{3} x^{2}, 0 \leq x \leq \frac{1}{2}

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

f (x) = - 2 x^{3} + 36 x^{2} - 192 x + 4

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