The Mean Value Theorem is a generalization of Rolle's Theorem (covered yesterday). In Rolle's Theorem, the function had to have the same y coordinate at the endpoints of the interval. The Mean Value Theorem addresses a function over any interval and essentially says that the average (mean) rate of change of a function over some interval will equal the instantaneous rate of change of the function somewhere in the interval.
You will see some generic problems finding the c value guaranteed by the MVT. We will also work some proofs using the MVT. One mathematical method of proof that you will need to use is called "Proof by Contradiction" and I worked an example of this in class today.
Notes from today are below.
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