4. Consider (1) if I € (0,1) where :[0,1] (0.1), 147 lc-e if2 € [1,1] and ce (0,2) C (a) Find the fixed points of (1) in

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4 Consider 1 If I 0 1 Where 0 1 0 1 147 Lc E If2 1 1 And Ce 0 2 C A Find The Fixed Points Of 1 In 1 (30.89 KiB) Viewed 29 times

4. Consider (1) if I € (0,1) where :[0,1] (0.1), 147 lc-e if2 € [1,1] and ce (0,2) C (a) Find the fixed points of (1) in terms of parameter c. (b) Investigate whether the fixed points identified in (a) are locally asymptotically stable. 17 marks (e) Let I<c< 2. Show that 0, lie: The and are period-two points of (1) [7 marks) A (d) For g e C let h(x) = g" (), n E N, be the n-fold composition of g with itself. Show that h'(x) = s'(g" (*))g'6943(x)). ...g'(x). where! - (e) Investigate whether the non-trivial period-two points identified in (c) are locally asymptotically stable.