2.3: Mean Value Theorem
Identifying maximum and minimum can be a challenging aspect of calculus, especially with complex polynomial and trigonometric functions. These points are valuable to determine when there is a maximum profit or height as well as a minimum loss. There is a specific theorem that can help us determine these values in an efficient manner.
Subunit 2.3 contains the mean value theorem, which is an important theorem in calculus, where a number exists on the interval that satisfies this theorem. Another important part of this theorem is determining when functions are continuous and differentiable.
Take notes as you watch this video. Listen to the presentation carefully until you are able to understand when a function is continuous and differentiable. The mean value theorem is also a point of focus that you need to understand and apply as well.
Read this section on extrema and the mean value theorem. Watch all of the videos within the section. At the end of the instruction, you should be able to apply and understand concepts of differentiability and continuous functions as well as theorems related to these concepts. Complete review questions 1-9 at the bottom of the page. These exercises will provide you with the opportunity to find extrema and apply Rolle's and mean value theorems. The solutions to these problems are located here.
Please click on the link above, and read the material on describing an application of a derivative and the mean value theorem, stopping at "Summary of Questions." This literacy component will allow you to further explore the concepts of a derivative and the mean value theorem. Write a one-page summary that discusses the key components of the article.