In Problems 1 through 12 first solve the equation f (x) = 0 to find the critical points of the given autonomous differential equation dx/dt = f (x) Then analyze the sign of f (x) to determine whether each critical point is stable or unstable, and construct the corresponding phase diagram for the differential equation. Next, solve the differential equation explicitly for x(t) in terms of t. Finally, use either the exact solution or a computer-generated slope field to sketch typical solution curves for the given differential equation, and verify visually the stability of each critical point.

dx dt = (x - 1)