Consider a unity negative feedback system with the open-loop transfer function

\[K G(s)=\frac{K}{s(s+3)(s+6)}\]

a. Use MATLAB to draw the Bode plots for \(K=1\). Determine the range of \(K\) for which the closed-loop system will be stable.

b. Determine the range of \(K\) for closed-loop stability by sketching the root locus.

c. Using Routh's criterion, determine the range of \(K\) for closed-loop stability.