Indicate which equilibria are stable and which are unstable

Question

Consider a population x_t with per capita producion (r)(x_t/1.0 + x_t²). After weiting the discrete-time dynamical system, do the folling for the given values of the parameter r=2.5

1. Find the equilibria

2. Graph the updating function

3. Indicate which equilibria are stable and which are unstable, and check via the slope criterion for stability

4. Describe in words how the population would behave.