#ATTENDANCE QUIZ FOR LECTURE 9 of Dr. Z.'s Math336 Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p9
#with an attachment called
#p9FirstLast.txt
#(e.g. p9DoronZeilberger.txt)

#Right after attending the lecture, but no later than 4:00pm that day

#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Q1. Using maple, find the fixed points of x->3.6*x*(1-x) (if they exist) (ii) Find stable fixed points then by hand

A1. (i)f:=3.6*x*(1-x);
                       f := 3.6 x (1 - x)
FP(f,x)
                       [0., 0.7222222222]
SFP(f,x)
                               []
(ii) x=3.6x-3.6x^2 -> 0=2.6x-3.6x^2 -> 0=x(2.6-3.6x) -> x = 0, x = 2.6/3.6 FIXED POINTS

CHECK IF STABLE f'(x) = 3.6 - 7.2x -> f'(0) = 3.6 > 1, f'(2.6/3.6) = 3.6 - 5.2 = -1.6 |-1.6| > 1. No stable fixed points. 

Q2. What other constant did Feigenbaum discover, and what is its significance?

A2. Feigenbaum's other Feigenbaum constant is his alpha constant (alpha = 2.502907875095892822283902873218...) This constant is the ratio between a width of a tine and the width of one of its subtines.