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Which of the following functions $f\left( x \right) $ satisfies the equations $f\left( x \right) f^{ ' }\left( x \right) =x$ and $f\left( 0 \right) =4$?

A

$f\left( x \right) =\sqrt { { x }^{ 2 }+16 } $

B

$f\left( x \right) =-\sqrt { { x }^{ 2 }+4 } $

C

$f\left( x \right) ={ x }^{ 2 }+4$

D

$f\left( x \right) =\sqrt { 16-{ x }^{ 2 } } $

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