What is the extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2 ?

The extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2 is

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extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2

extreme points

f (x, y) = 3 x^{- 2} + 5 y^{- 2} + 8 x y^{2}

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = 16 x + \frac{30}{y ^{4}}

D (x, y) = \frac{18 ( 16 x y ^{4} + 30 )}{x ^{4} y ^{4}} - 256 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) = 4 x^{4} + 4 y^{4} - x y

f (x) = ln (x + y)

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

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

f (x) = x^{3} - 3 x^{2} - 9 x + 10

What is the extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2 ?
The extreme f(x,y)=3x^{-2}+5y^{-2}+8xy^2 is