Exercise 104

Suppose $\frac{dx}{dt} = (x-\alpha)(x-\beta)$ for two numbers $\alpha < \beta$.

1. Find the critical points, and classify them.

For b), c), d), find $\displaystyle \lim_{t\to\infty} x(t)$ based on the phase diagram.

1. $x(0) < \alpha$,
2. $\alpha < x(0) < \beta$,
3. $\beta < x(0)$.