Question

Fixed points of f?
f(x) = x^2+13/12x - 1/2

a) use algebra to find the fixed points and classify them.

b) use the gradient criterion to determine an interval of attraction for one of the fixed points of f

c) find exact values of the 2nd and 3rd terms of the sequence xn obtained by iterating f with initial term x0= 0 (express your answer as fractions in their lowest terms) State the long term behaviour of this sequence.

Thank for your help with this!

Answer 1

a fixed point is a point where x=f(x)
In this case

x= x^2+13/12x - 1/2 solve for x.

gradient of attraction: when gradient is +

http://mathworld.wolfram.com/FixedPoint.html

Answer 2

Can someone please help answering the last part of the question I'm stuck:

c) find exact values of the 2nd and 3rd terms of the sequence xn obtained by iterating f with initial term x0= 0 (express your answer as fractions in their lowest terms) State the long term behaviour of this sequence.