The continuous random variable \(X\) has probability density function \(f\) given by
\(f(x)=\left\{\begin{array}{ll} \frac{1}{128}\left(4ax-bx^{3}\right) & 0 \leqslant x \leqslant 4 \\ c & 4 \leqslant x \leqslant 6 \\ 0 & \text{otherwise} \end{array}\right.\)
where \(a\), \(b\) and \(c\) are constants.

The upper quartile of \(X\) is equal to 4.

(a) Show that \(c=\frac{1}{8}\) and find the values of \(a\) and \(b\).

(b) Find the exact value of the median of \(X\).

(c) Find \(\mathrm{E}(\sqrt{X})\), giving your answer correct to 2 decimal places.