As shown in the diagram, the continuous random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{ll} m x & 0 \leqslant x \leqslant 2, \\ \frac{k}{x^{2}}+c & 2 \leqslant x \leqslant 6, \\ 0 & \text { otherwise, } \end{array}\right.\)
where \(m, k\) and \(c\) are constants.
(a) Given that \(\mathrm{P}(X \leqslant 2)=\frac{1}{3}\), show that \(m=\frac{1}{6}\) and find the values of \(k\) and \(c\).

(b) Find the exact numerical value of the interquartile range of \(X\).