title: Finding the upper bound of a mathematical function (function analysis)
body: <p>I am trying to understand Big-O notation through a book I have and it is covering Big-O by using functions although I am a bit confused. The book says that O(g(n))  where g(n) is the upper bound of f(n). So I understand that means that g(n) gives the max rate of growth for f(n) at larger values of n.</p>
  
  <p>and that there exists an n_0 where the rate of growth of cg(n) (where c is some constant) and f(n) have the same rate of growth.</p>
  
  <p>But what I am confused is on these examples on finding Big O in mathmatical functions.</p>
  
  <p>This book says findthe upper bound for f(n) = n^4 +100n^2 + 50
  they then state that n^4 +100n^2 + 50 &lt;= 2n^4 (unsure why the 2n^4)
  then they some how find n_0 =11 and c = 2, I understand why the big O is O(n^4) but I am just confused about the rest.</p>
  
  <p>This is all discouraging as I don't understand but I feel like this is an important topic that I must understand.</p>
  
  <p>If any one is curious the book is Data Structures and Algorithms Made Easy by Narasimha Karumanchi</p>
  
  <p>Not sure if this post belongs here or in the math board.</p>