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!