Integer point of local extremum not implies point of local extremum among integers

Statement

It is possible to have a continuous function $f$ (in fact, we can choose $f$ to be a polynomial function) and an integer $n$ such that all these hold:

• The interval $[n-1,n+1]$ is in the domain of $f$
• $n$ is a point of local extremum for $f$.
• $n$ is not a point of local extremum among integers for $f$.

Related facts

Opposite facts

• Integer point of absolute extremum implies point of absolute extremum among integers

Similar facts

• Point of absolute extremum among integers need not be near point of absolute extremum