Science:Math Exam Resources/Courses/MATH103/April 2016/Question 06 (b) (iii)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) (i) • Q6 (a) (ii) • Q6 (a) (iii) • Q6 (a) (iv) • Q6 (a) (v) • Q6 (b) (i) • Q6 (b) (ii) • Q6 (b) (iii) • Q7 (a) (i) • Q7 (a) (ii) • Q7 (b) (i) • Q7 (b) (ii) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) •
Question 06 (b) (iii) 

(iii) Classify the fixed points in (ii) as stable or unstable. Justify your answers. 
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 

Evaluate the derivative of the map at the fixed points. 
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. In part (ii), we showed that the fixed points of are In order to classify these points, we first need to find the derivative of . Clearly, At the point we have So, this fixed point is stable. At the point we have So, this fixed point is stable also. 
Please rate how easy you found this problem:
Current user rating: 100/100 (1 votes) Hard Easy 