The first two problems on this quiz are simply vocabulary. This top equation is a differential equation, as it has both functions and their derivatives mixed in This equation has no derivatives in it and is not a differential equation Differential equations are used to model flows The second equation is a difference equation Difference equations are used to describe or model maps Question 3 asks us to characterize each of these four fixed points as stable, unstable, or chaotic As it makes no sense to have a chaotic fixed point, we can eliminate this choice from all of the questions To analyze whether these fixed points are stable or unstable, we need to know whether a small perturbation near the fixed point grows or shrinks For this first fixed point, notice that a small perturbation quickly shrinks down and the pendulum returns to the original fixed point So this fixed point is stable. That is the answer to 3a For this fixed point in figure 1b, notice that the small perturbation caused by my finger rapidly grows That means this fixed point is unstable. That is the answer to 3b Notice for c and d, I have to hold them in position That is, they are so unstable, I cant even get them to balance at this point That should give you a hint as to the answer for these problems But to make it very clear, watch small perturbations of both c and d As you can see, both c and d are also unstable fixed points. That is the answer to 3c and 3d