Point of local extremum among integers

Definition

Suppose $f$ is a function whose domain of definition contains an integer $n$ as well as the integers $n-1$ and $n+1$. We say that $n$ is a point of local extremum among integers for $f$ if it is either a point of local maximum among integers or a point of local minimum among integers Both notions are defined below.

Point of local maximum among integers

We say that $n$ is a point of local maximum among integers for $f$ if $f(n)\ge f(n-1)$ and $f(n)\ge f(n+1)$.

Point of local minimum among integers

We say that $n$ is a point of local minimum among integers for $f$ if $f(n)\le f(n-1)$ and $f(n)\le f(n+1)$.