Consider the eventual fixed points of the logistic map $Lµ : [0, 1] → [0, 1], Lµ(x) = µx(1 − x)$, for $0 <µ< 4.$
Show that there are additional eventual fixed points associated with $x = 1 − 1/µ$ when $2 <µ< 3$
suppose $µ = 11/4$ , and $(11/4) x(1-x) = x$, then $-11x^2 + 7x = 0$ which gives $x = 0$ and $x= 7/11$, does that mean that $0$ and $7/11$ are eventualy fixed points?
How can I prove there are more additional eventually fixed points within $2 <µ< 3$