This is from Calculus by Michael Spivak, 3rd Edition, Chapter 11, problem 5. The solution published in the Answer Book seems to be incomplete. I think my solution is right and just want to verify.
11-5. For each of the following functions, find all local maximum and minimum points. (iv) $f(x) = \begin{cases} 1, &x = 1/n\text{ for some $n$ in $\mathbb{N}$} \\ 0, &\text {otherwise.} \end{cases}$
Here is the Answer Book solution and my proposed edit:
(iv) All $1/n$ for $n$ in $\mathbb{N}$ are local maximum points, and all other $x$ are local minimum points.
Revision All $1/n$ for $n$ in $\mathbb{N}$ are in $[0,1]$, and are local maximum points (including $1$). All other $x$ in $[0,1]$ are local minimum points (including $0$). All $x$ not in this interval are both local maximum and local minimum points.