In general (without substituting numerical values for s and r), can both equilibria be stable? What happens if r = s?
Recall the updating function with the fraction p of mutant bacteria given by

where s is the per capita production of the mutant and r is the per capita production of the wild type. Find the derivative in the following cases, and evaluate at the equilibria p = 0 and p = 1. Are the equilibria stable?

f(p) = sp + r(1-p)