If f is a constant function and (a,b) is any open interval, prove that f(c) is both a local and an absolute ex

If f is a constant function and (a,b) is any open interval, prove that f(c) is both a local and an absolute extremum of f for every number c in (a,b).

If f is a constant function and (a,b) is any open interval, prove that f(c) is both a local and an absolute ex
This is checking the definitions carefully.





Local: f'(c) = 0 since f is constant. Since the domain (a,b) is an open interval, there are always c1 %26lt; c %26lt; c2 with f(c) %26gt;= f(c1) and f(c2), same for %26lt;=.





Global: For every x in (a,b), f(c) %26gt;= f(x) (global max) and f(c) %26lt;= f(x) (global min)