(Solved): please show clear step by step how to solve!  Consider the unity negative feedback system shown ...

Consider the unity negative feedback system shown in Fig. 1. Figure 1: A block diagram for Problem 2 (a) Find the range of \( K \) for which the closed-loop system will be BIBO stable with \[ G(s)=\frac{K}{s(s+1)(s+6)} . \] (b) Find the range of \( K \) for which the closed-loop system will be BIBO stable with \[ G(s)=\frac{K(s+1)}{s(s-2)(s+6)} . \] (c) Find the range of \( K \) where \( K>0 \) for which the closed-loop system will be BIBO stable with \[ G(s)=\frac{K(s-2)}{(s+1)\left(s^{2}+6 s+10\right)} . \] (d) Find the range of \( K \) for which there will be only two closed-loop, ORHP poles with \[ G(s)=\frac{K(s+2)}{\left(s^{2}+1\right)(s+4)(s-1)} . \] \( { }^{1} \) OLHP: open left half plan, ORHP: open right half plane.