For \(x > 0\), the acute region between \(y = \frac{x}{4}\) and \(y = \frac{x}{2}\) is \(\frac{x}{4} < y < \frac{x}{2}\).

Put \(x = a^2\), \(y = a\): \(\frac{a^2}{4} < a < \frac{a^2}{2}\).

• \(a < \frac{a^2}{2} \Rightarrow a > 2\) (for \(a > 0\))
• \(\frac{a^2}{4} < a \Rightarrow a < 4\)

So \(a \in (2, 4)\).

Answer: (C)