Science:Math Exam Resources/Courses/MATH103/April 2017/Question 07 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) (i) • Q1 (e) (ii) • Q1 (e) (iii) • Q1 (f) • Q2 (a) • Q2 (b) (i) • Q2 (b) (ii) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 • Q5 • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) •
Question 07 (b) 

The figure below shows the graph and the diagonal (dashed line). Use this plot to answer the following questions: (b) Determine the stability of each fixed point. (Explain your reasoning.) 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

A fixed point of is stable if and only if . 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution  

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. When , the slope of that point should be parallel to or . This means that a line that is flatter than satisfies , and therefore that the the fixed point is stable; a line that is steeper than satisfies The coordinates for 4 fixed points is . Answer:
