title: For inputs of size n, for which values of n does insertion-sort beat merge-sort?
body: <p>In the book Introduction to Algorithms (Corman), exercise 1.2-2 asks a the following question about comparing  implementations of insertion sort and merge sort. For inputs of size n, insertion sort runs in 8n^2 steps while merge sort runs in 64n lg n steps; for which values of n does insertion sort beat merge sort?</p>
  
  <p>Although I am interested in the answer, I am more interested in how to find the answer step by step (so that I can repeat the process to compare any two given algorithms if at all possible). </p>
  
  <p>At first glance, this problem seems similar to something like finding the break even point in business-calculus, a class which I took more than 5 years ago, but I am not sure so any help would be appreciated. </p>
  
  <p>Thank you</p>
  
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  P/S If my tags are incorrect, this question is incorrectly categorized, or some other convention is being abused here please limit the chastising to a minimum, as this is my first time posting a question.  </p>