Science:Math Exam Resources/Courses/MATH103/April 2014/Question 09 (a)
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Question 09 (a) 

Consider the iterated map where for . Find all fixed points of the iterated map and determine their stability. Hint: use to check stability. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

A fixed point of is a point for which . 
Hint 2 

A fixed point of is stable whenever and unstable when . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The fixed points are solutions to , i. e. . Thus, either or , i. e. . Now a fixed point is stable if and unstable if . Since , we have
Thus 0 is an unstable fixed point and 1/3 is a stable fixed point. 