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Use Lagrange Multipliers to find the only critical point of:

$$f(x,y)={ x }^{ 2 }y-\ln { (\left| x \right|) }$$

...subject to the constraint $8x=-3y$.

A

$(\frac { 1 }{ 3 } ,\frac { -8 }{ 9 } )$

B

$(\frac { 1 }{ 2 } ,\frac { -4 }{ 3 } )$

C

$(-3,8)$

D

$(\frac { -1 }{ 2 } ,\frac { 4 }{ 3 } )$

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