7
votes
Accepted
Number of real roots of the n-th iteration of $f(x) = x^3 - 3x + 1$
We study the number of real roots of the nth iterate of the function $f(x)=x^3-3x+1$.
First compute $f'(x)=3x^2-3=3(x^2-1)$, so $f$ increases on $(-\infty,-1]$, decreases on $[-1,1]$, and increases ...
- 3,478
Only top scored, non community-wiki answers of a minimum length are eligible