When I learn some basic ergodic theory, I encounter an interesting exercise. As we all know, 3-periodic point often means chaos. Therefore, when a continuous map has a 3-periodic point, it may have positive topological entropy. The following question exactly talks about it.

Question: Let $ I=[0,1]$, and $f$ be a continuous map from $I$ to itself. Suppose $f$ have a 3-periodic point, where 3 means minimal period. Then try to prove the topological entropy of $f$ is strictly positive.

Well, Sharkovsky's theorem tells us that $f$ has arbitrary periodic points, which means "chaos". But I do not know how to prove this exercise.

My idea is to construct a symbolic system as a factor or sub-system by dividing the interval with periodic points, for Bernoulli shift has positive topological entropy. But I fail. Please help me! Thank you!