State the Mean Value Theorem, including the conditions.
Construct examples demonstrating the necessity of the conditions in the Mean Value Theorem.
Video3.2.1.Mean Value Theorem.
In this video we introduce one of the most important theorems in calculus: the Mean Value Theorem. This theorem connects a local property (the derivative) to a global property (the slope over an interval). We will see examples showing the necessity of the assumptions in this theorem.
Post-video reflection.
Can you come up with a counterexample to the theorem in the case where f(x) was continuous only on the open interval (a,b) and not the closed interval [a,b]?
