If f is the function, f(x) = (1/2)x^2 +2x - (5/8) a) use algebra to find the fixed points of f and classify them as attracting or repelling?
for a) i have found the 2 fixed points of (1/2) or 0.5 and (-5/2) or -2.5
which i have classified as both attracting as they are <1
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 x0= -(7/2) express as fractions in their lowest terms, hence state the long term behavior of this sequence and explain
for c) i get x1 = -3/2
x2 = -5/2
presuming that x0 is first term and x1 is second term and x2 is third term
i am really stuck on part b) if anyone can help and if any one can point out if part a) and c) are correct i would really appreciate it
for b) ive now found that for fixed point 1/2 using the gradient criterion we get
-1<(1/2x)+(2)<1
which gives us -1<(1/2x)+2=-6<x
(1/2x)+2<1=-2<x
thus -6<x<-2
so interval of attraction for fixed point 1/2 is (-6,-2)