Here are the main points that will be addressed in the videos. Please read these and think about them as you watch.

• The mean value theorem is a statement about when the instantaneous rate of change of a function at a point is equal to the average rate of change of that function on an interval.
• The conditions for the mean value theorem to apply are:
  • $f$ is defined on the closed interval $[a,b]$,
  • $f$ is continuous over the closed interval $[a,b]$, and
  • $f$ is differentiable over the open interval $(a,b)$
• The mean value theorem says that when the conditions above are satisfied, then there is a number $c$ in $(a,b)$ where $$f'(x) = \dfrac {f(b)-f(a)}{b-a}$$