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) = 4 x^{3} e^{- x}

f (x) = x^{3} + y^{3} - 36 x y

f (x, y) = 400 - 16 x^{2} - 36 y^{2}

f (x) = 7 sin (x) + 7 cos (x)

f (x) = 5 sin (x) + 5 cos (x), 0 \leq x \leq 2 π

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)