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?
