Relative/Absolute maxima/minima

[Loki123]

This source: https://www2.math.binghamton.edu/lib/exe/fetch.php/people/mckenzie/bittinger_et_al..pdf
page: 201
this picture:
why both absolute and relative minimums marked as relative, but only one maximum is marked as relative??

 

[Zermelo]

Depends on the definition of relative (local) extrema. Usually it’s defined as a point x such that every point y from it’s neighborhood (x-e, x+e) f(x) >= f(y). And this point is on the edge, so it doesn’t have a valid neighborhood, the function f isn’t defined to the right of it. That’s my guess at least
It might also be a mistake

 

[R.M.]

If c is a relative maximum inside some interval (a, b), then it must be strictly inside that interval (called an open interval), and therefore cannot be at an endpoint. Same applies for a relative minimum. a < c < b.