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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{4}{x y ^{3}}

D (x, y) = \frac{12}{x ^{4} y ^{4}}

Check the sign of at each critical point

Check critical point

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

Minimum

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

x e^{- x^{2}}

f (x) = 2 x^{3} + 12 x^{2} - 72 x + 11

f (x, y) = x^{4} + 6 y - 10

f (x, y) = x ln (y)

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 2

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