At What Value of X Does the Function $f ( x ) = 3 x - \sqrt [ 3 ] { x }$

At what value of x does the function $f ( x ) = 3 x - \sqrt [ 3 ] { x }$ change from increasing to decreasing?

A) $\frac { 1 } { 8 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 27 }$
E) $\frac { 1 } { 9 }$
F) $\frac { \sqrt { 3 } } { 4 }$
G) $\frac { \sqrt { 3 } } { 3 }$
H) $\frac { 1 } { 32 }$

Correct Answer:

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