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​​​​​Consider a unity negative feedback control system with forward path gain $G(s)=\frac{K}{(s+1)(s+2)(s+3)}$ as shown.



The impulse response of the closed-loop system decays faster than $e^{-t}$ if $\_\_\_\_\_\_$.

  1. $1 \leq K \leq 5$
  2. $7 \leq K \leq 21$
  3. $-4 \leq K \leq-1$
  4. $-24 \leq K \leq-6$

 

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