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

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

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

extreme

Minimum (\frac{1}{2}, 2)

Solution steps

Find the critical points:

(\frac{1}{2}, 2)

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

D (x, y) = \frac{16}{x ^{3} y ^{3}} - 4

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, 2) :

Minimum

Minimum (\frac{1}{2}, 2)

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