Stanford math tournament cubic question

Описание: Enhance your math contest skills from Brilliant: 👉https://brilliant.org/blackpenredpen/ (20% off with this link!)

This question is from the Stanford Math Tournament (SMT) the algebra tiebreaker section https://www.stanfordmathtournament.co.... We are given a cubic function f(x)=x^3-6x^2+25/2x-7 and we know there exists a closed interval [a,b] such that the sequence x, f(x), f(f(x)), ... is bounded for x on [a, b]. This question is fascinating because not all cubic functions have such properties. I will use the fixed-point approach for this problem, how would you solve this? #brilliant #math #stanford #blackpenredpen

0:00 Stanford Math Tournament algebra tiebreaker
1:00 Check out Brilliant
2:10 My solution to this problem
7:12 Why my solution works for this problem
Note: I avoided calculus derivative here because I wanted to keep it with just algebra. I will do another video on the fixed-point iteration later.
9:56 the official solution

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