Project #21082 - functions

 

In this question, f is the function

f(x) = 1/3x^2 -1/6x +5/6

 

 

(a) Use algebra to find the fixed points of f, and to classify them as

attracting, repelling or indifferent. 

 

(b) Use the gradient criterion to determine an interval of attraction for

one of the fixed points of f. 

 

(c) Find the exact values of the second and third terms of the sequence

xn obtained by iterating f with initial term x0 = 2. (Express your

answers as fractions in their lowest terms.) Hence state the long-term behaviour of this sequence, explaining your reasoning. 

Subject Mathematics
Due By (Pacific Time) 01/18/2014 12:48 pm
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