Backward taylor expansion



Dear everybody,
I just installed maxima, which a want to use primarily to do some 
numerical analysis.
I am trying to get a classical forward and backward taylor expansion:

f(x+h) = f(x) + (df(x+h) / dx) | h=0 * h +  (d2f(x+h) / dx2) | h=0 * 
h^2/2 + ...
f(x-h)  = f(x) + (df(x-h) / dx) | h=0 *  h +  (d2f(x-h) / dx2) | 
h=0  * h^2/2 + ...

Now here is the problem:
apparently I can get the two truncated series with the taylor 
command, but I found no way to sum them up in a user-friendly way.
I tried:

taylor(f(x+h),h,0,2) - taylor(f(x-h),h,0,2)

then, in the first order term, i get:

df(x+h)/dh | h=0 - df(x-h)/dh | h=0

and I found no way to tell maxima that this term should simplify to 
zero. I guess this is because maxima assumes that my function could 
in principle have a discontinuous derivative... how can I solve the 
problem? Any help would be very appreciated.
Thank you
Fabio