1. ## Finding fixed points - help please!

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!

2. Originally Posted by Chamberlain
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!
Well, what have you tried so far? Since a fixed point is a solution of $x=f(x)$ what does that suggest as a starting point for (a)?

CB

3. Originally Posted by CaptainBlack
Well, what have you tried so far? Since a fixed point is a solution of $x=f(x)$ what does that suggest as a starting point for (a)?

CB
Well I have solved it and then applied the quadratic formula:
$12x^2+13x-6=0$ which is $-13/24\pm1/24
\sqrt 457
$

....so is what I have done correct in terms of finding fixed points? It feels wrong as I have only found the x-axis intersection...I'm a bit lost on this one... my book does not explain this clearly... thanks for your help!