A population p(t) satisfies dp/dt = f(p), where f(p) = kp (1-p/a)(1-p/b)
The population lies in the interval 0<=p<=b
k,a,b are positive constants with b>a
Determine all equilibrium points.
For this part f(p)=0 so p=0, p=a, p=b
Then I have to sketch f as a function of p. I know by expanding f(p) that is a cubic equation but I don't have any data about k,a,b except that they are all >0.
I found f'(p) and solved it to be equal to zero to find the stationary points, i found an answer but was a complete mess. I don't know what we are expected to sketch exactly without any further information.
I will appreciate any help. Thanks in advance!