Application Of Derivatives

Consider the function \(f:\left[\frac{1}{2}, 1\right] \rightarrow \mathbb{R}\) 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