Example 2 (a).  Compute numerical approximations for the derivatives , using step sizes .  
2 (b).  Plot the numerical approximation over the interval .  Compare it with the graph of over the interval .  

Solution 2.

2 (a).  Compute numerical approximations for the derivatives ,  using step sizes .  

f'[x]

Where are the best approximations in this table.  

2 (b).  Plot the numerical approximation   over the interval  .  Compare it with the graph of    over the interval  .

(c) John H. Mathews 2004