I want to determine if the function $\{nsin\frac{1}{n}\}^{\inf}_{n=1}$ is increasing or decreasing, in order to find supremum and infimum (and decide if maximum and minimum exist).
So the first thing I have to do to be able to decide supremum, infimum and if max and min exist is to find out if the function is increasing or decreasing but how do I do this without using my graphing calculator? My first thought was to find the zeros for the derivative and check this but there are no zeros for the derivative (or at least that could not be found with a calculator).
Thanks in advance!