6.2. Let $f(x)=x^{2}+p x+q$. It is known that the inequality $|f(x)|>\frac{1}{2}$ has no solutions on the interval $[2 ; 4]$. Find $\underbrace{f(f(\ldots f}_{2017}\left(\frac{5-\sqrt{11}}{2}\right)) \ldots)$. Round your answer to the nearest hundredth if necessary.
Answer: 4.16 (exact value: $\frac{5+\sqrt{11}}{2}$ ).