Suppose you used a Taylor series to evaluate/approximate f(x) with a "x" value.

My question is this - how would you know if the resulting approximation is less or more than the true value of f(x)? Also, am I right in assuming that if the series is alternating, then if the last term is negative then the approximation is less than f(x) and vice versa? But what about non-alternating Taylor series?

Also, on a completely different subject, what are some of the recommended self-study multivariable calculus books? I'm thinking about getting a headstart in multivariable calculus in the summer, so any recommendations?