Consider the function $f : \left[ \frac { 1 } { 2 } , 1 \right] \rightarrow \mathrm { R }$ defined by $f ( x ) = 4 \sqrt { 2 } x ^ { 3 } - 3 \sqrt { 2 } x - 1$. Consider the statements\\
(I) The curve $y = f ( x )$ intersects the $x$-axis exactly at one point\\
(II) The curve $y = f ( x )$ intersects the $x$-axis at $x = \cos \frac { \pi } { 12 }$\\
Then\\
(1) Only (II) is correct\\
(2) Both (I) and (II) are incorrect\\
(3) Only (I) is correct\\
(4) Both (I) and (II) are correct