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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = \frac{8}{x ^{3} y ^{3}} - 16

Check the sign of at each critical point

Check critical point

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

Minimum

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

f (x) = x^{4} - 8 x^{3} + 6

f (x) = \frac{x ^{3}}{3 - x ^{2}}

f (x) = - \frac{6 x}{3 x ^{2} + 8}

f (x, y) = 2 x^{3} + y^{3} + 3 x^{2} - 3 y - 12 x - 4

Y (A, B) = A B + A B + A B

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