Science:Math Exam Resources/Courses/MATH103/April 2015/Question 06 (b)
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Question 06 (b) 

Consider the function , where is a parameter. Now consider the iterated map for . (b) Determine the range of for which each fixed point (steady state, equilibrium) is stable. 
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 . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that in part (a), we find the fixed points of , . By the definition of a stable fixed point in Hint, we first find the derivative of : . Then, we can get
and . Therefore, is stable if , while is stable if (.)
