What is the extreme f(x,y)=xy+2/x+4/y ?

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

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extreme f(x,y)=xy+2/x+4/y

extreme points

f (x, y) = x y + \frac{2}{x} + \frac{4}{y}

Minimum (1, 2)

Solution steps

Find the critical points:

(1, 2)

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

D (x, y) = \frac{32}{x ^{3} y ^{3}} - 1

Check the sign of at each critical point

Check critical point

(1, 2) :

Minimum

Minimum (1, 2)

f (x, y) = - 5 x^{2} - 8 y^{2} - 2 x y + 42 x + 102 y

\frac{12}{x ^{2} + 1}

f (x) = cos (x) - 2 x, 0 \leq x \leq 4 π

f (x) = \frac{7 ( x - 1 ) ^{2}}{x + 9}

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}

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