Consider the function \( f : \left[ -\frac{1}{2}, 1 \right] \to \)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:
