Problem 3         Due 1/31/00

In this problem we examine the combination of
algorithm error and machine round off error.  A
rather bizzare formula for calculating the
derivative of a function is given by:

df/dx = (-3f(x)+4f(x+h)-f(x+2h))/2h

(Actually, this is very useful as an approximation
to a derivative at x when the function cannot be
evaluated for arguments less than x)

Determine the error this formula makes in calculating
the derivative of f(x)=exp(x) over the range 0:.1,
and determine both the minimum error and the optimum
value of h.  How does this compare to the forward
difference formula?