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 points

f (x, y) = 2 x y + \frac{1}{x} + \frac{4}{y}

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)

f (x) = x^{4} - 5 x^{2} = x^{2} (x^{2} - 5)

f (x) = x ln (8 x)

x 7 - x

f (x) = 2 cos (2 x) - 2

2 x e^{- x^{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)