Consider approximating
the derivative of the function for **x=1**. Use the forward and
central difference quotients as defined below.

Using
both single and double-precision programs, make tables showing in
each case the value for **h**, the difference approximations and
, and the errors associated with these values (since we know
the answer here). Use a wide range of values for the difference
interval **h**: from to . What can you say about the quality of
the two different approximations and their associated optimal values
for **h**? Can you suggest how an optimal value for **h** can be estimated?