For a suitably nice, real-valued function "f" defined on an open interval containing [a,b], f(b) can be expressed as p[subscript n](b) (the nth Taylor polynomial of f centered at a) plus an error term of the (Lagrange) form f[superscript (n+1)](c)(b-a)[superscript (n+1)]/(n+1)! for some c in (a,b). This article is for those who think that not much more can be said about where in (a,b) c is located. Supplementary materials, including further numerical illustrations and sketches of some proofs, are available at http://faculty.colostate-pueblo.edu/rick.kreminski.