Quasiconcave and single-peak

Question

Let $f$ be a funtion from $\mathbb{R}$ to $\mathbb{R}$ is quasiconcave. I would like to see why $f(x)$ is either monotonic or single peak. I know that if $f(x)$ is not monotonic then there exists $x > y > z$ such that $f(y) > f(x)$ and $f(y) > f(z)$. By quasi concavity, $f(t)$ is decreasing for all $t \notin [y,z]$. However, I don't know how to prove there is a peak in $[y,z]$ to conclude $f$ is single-peak.