title: What's the upper bound of f(n) = n^4 + 100n^2 + 50?
body: <p>I'm solving some exercises related to Big-O and I'm stuck on this one:</p>
  
  <pre><code>Exercise - Find upper bound for f(n) = n^4 + 100n^2 + 50
  </code></pre>
  
  <p>I tried to solve it step by step but something is wrong ...:</p>
  
  <pre><code>1.=&gt; n^4 + 100n^2 + 50 &lt;= O(g(n))
  2.=&gt; n^4 + 100n^2 + 50 &lt;= Cn        ** Added -n^4 to both sides
  3.=&gt; n^4 + 100n^2 + 50 -n^4 &lt;= Cn -n^4
  4.=&gt; 100n^2 + 50 &lt;= Cn - n^4         ** Put n in common
  5.=&gt; 100n^2 + 50 &lt;= n(C - n^3)       ** Divided n in the opposite site
  6.=&gt; (100n^2 + 50)/n &lt;= C -n^3       ** Assumed 1 for n
  7.=&gt; 100 + 50 &lt;= C - 1                      
  8.=&gt; 151 &lt;= C
  </code></pre>
  
  <p>There is something wrong because the answer is c = 2 and n=11. I saw this very same question being asked on stackoverflow but without a step by step solution</p>