What is the extreme 1/(x^2)+4/(y^2)+4xy^2 ?

The extreme 1/(x^2)+4/(y^2)+4xy^2 is

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extreme 1/(x^2)+4/(y^2)+4xy^2

extreme points

\frac{1}{x ^{2}} + \frac{4}{y ^{2}} + 4 x y^{2}

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = 8 x + \frac{24}{y ^{4}}

D (x, y) = \frac{6 ( 8 x y ^{4} + 24 )}{x ^{4} y ^{4}} - 64 y^{2}

Check the sign of at each critical point

Check critical point

Minimum

Check critical point

Minimum

Check critical point

Minimum

Check critical point

Minimum

f (x, y) = x^{2} + x y + y^{2} - 7 y + 16

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

f (x) = 3 x^{5} - 5 x^{3} + 2

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

What is the extreme 1/(x^2)+4/(y^2)+4xy^2 ?
The extreme 1/(x^2)+4/(y^2)+4xy^2 is