Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 14E / b / Solution

The homogeneous equilibria are $0,r,1$. Since $f\prime (0)=-r<0$, $f\prime (1)=r-1<0$, and $f\prime (r)=r(1-r)>0$, the first and last are linearly stable and the middle one unstable.

Solved by gpt-5.6-sol high.