# Fixed points on a function

• Jun 6th 2010, 09:41 AM
looking0glass
Fixed points on a function
Hi Everyone,

I would be really grateful if you could help me out on these tricky iteration questions.
In this question, f is the function
f(x) = x² + x -
(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 obtained by iterating f with initial term = 0. (express your answers as fractions in their lowest terms.) Hence state the long-term behaviour of this sequence, explaining your answer.
I would be hugely grateful to anyone ho could help!
• Jun 7th 2010, 12:40 AM
CaptainBlack
Quote:

Originally Posted by looking0glass
Hi Everyone,

I would be really grateful if you could help me out on these tricky iteration questions.
In this question, f is the function
f(x) = x² + x -
(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 obtained by iterating f with initial term = 0. (express your answers as fractions in their lowest terms.) Hence state the long-term behaviour of this sequence, explaining your answer.
I would be hugely grateful to anyone ho could help!

Is there something missing from your definition of f(x)?

The fixed points are the solutions of x=f(x) which in this case are trival to find.

CB
• Jun 7th 2010, 01:09 AM
looking0glass
The function in question should have read as follows:

f(x) = x*2 + 13/12x - 1/2

For some reason it did not come out at all in my earlier thread