Taylor's Theorem/One Variable with Two Functions

Applications
You can derive multiple forms of the remainder term from this formulation:
 * Lagrange Form of the Remainder comes from taking $k = n$ and $\map g x = \paren {x - a}^{n + 1}$.
 * Cauchy Form of the Remainder comes from taking $k = 0$ and $\map g x = x - a$.