Increasing function theorem an alternative for the mean value theorem

This thesis is based on the article Rethinking Rigor in Calculus: The Role of the Mean Value Theorem by Thomas W. Tucker. It gives a detailed proof of the Increasing Function Theorem independent of the Mean Value Theorem. The Increasing Function Theorem states that if f1(x) \u3e0 on an interval, then f is increasing on that interval. The Immediate Consequences of the Mean Value Theorem were redone using the Increasing Function Theorem so as to illustrate the usefulness of the Increasing Function Theorem. The derivation of Taylor Error Bounds was provided as one of the consequences of the Increasing Function Theorem. Here, the proofs are presented as simply as possible so that they will be understood by students of elementary calculus courses