
      third derivative as $f(x)=e^x$ does at $x=1$.</li>
    </ul>
  </div>

  <div class="comment">
    The problems above introduced the final idea. We will let
    $dx=x-c$ (a small change in $x$). Since the polynomial should be
    close to the function, a small change in $y$ is $dy=P_n(x)-f(c)$.
    We can write the Taylor polynomial notation above in the form 
    $$P_n(x) -
    f(c)=dy=\frac{f'(c)}{1!}dx+\frac{f''(c)}{2!}dx^2+\cdots
    +\frac{f^{(n)}(c)}{n!}dx^n. $$  If we want to estimate the
    