Consider the function = and divide the domain 0 ≤ ≤ 1 into m intervals. For the “exact” approximation of the function, we will use = 100 intervals.
Plot the “exact” function when = 4. Then starting with = 2 and increasing m gradually, plot the various approximations on the same plot as the exact function. How large must m be to discern the qualitative behavior of the exact function (i.e., have the same number of minima and maxima points)? Can you suggest a general criterion valid for any n that specifies the smallest m that still provides a qualitative approximation of the exact function?