Science:Math Exam Resources/Courses/MATH103/April 2013/Question 05 (b)/Statement

Consider the differential equation $\displaystyle {\frac {dx}{dt}}=4x^{3}-12x^{2}+8x$. Calculate the steady states (equilibria) and mark them in the sketch below. Find $\displaystyle x(t)$ for $\displaystyle t\to \infty$ for the initial points labeled a,b and c (see sketch).