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

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

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

extreme points

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

Minimum (2, 1), Maximum (- 2, - 1)

Solution steps

Find the critical points:

(2, 1), (- 2, - 1)

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

D (x, y) = \frac{128}{x ^{6} y ^{4}}

Check the sign of at each critical point

Check critical point

(2, 1) :

Minimum

Check critical point

(- 2, - 1) :

Maximum

Minimum (2, 1), Maximum (- 2, - 1)

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