Another Taylor series question



OK, I've got maxima 5.30.0 up and running.  Nice.  What I want to do is
define a function

t(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2 + f'''(a)(x-a)^3/6 + ...

that is, a Taylor series, but so that t(b), for example, produces

f(a) + f'(a)(b-a) + f''(a)(b-a)^2/2 + f'''(a)(b-a)^3/6 + ...

with the derivatives still in terms of x.  This is what happens at the
moment:

(%i1) t(x):=taylor(f(x),x,a,6);

(%i2) t(b);

and the derivatives now are all in terms of b.  Any ideas?  (I'd still like
to be able to differentiate and integrate t(x) in terms of x).

-Alasdair