Remainder of a polynomial In the remainder for a Taylor series the remainder involves a term wherein some number in the interval (x and our point a) is evaluated in the function's (n+1)th derivative. Why is it that it isn't possible to find this number?

In theory you can numerically determine the intermediate value that gives the largest or smallest bound by using numerical evaluations of functions and possibly their derivatives and solving a combination of optimization problems based on numerical function and derivative values. However finding the intermediate point that gives a bound with a formula will involve solving an optimization problem that involves combining a polynomial and a possibly very complex e.g. transcendental function, and in general those kinds of optimization problems cannot be solved analytically with a closed form formula.