AP Test Prep
College Board

Differentiability of Piecewise Defined Functions

For Teachers 10th - 12th
Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...
Lesson Plan
Curated OER

Worksheet 15-Fall 1995

For Teachers Higher Ed
In this math worksheet students use the intermediate value theorem to solve two problems. They find parallel lines that will cut a convex shape into two pieces with equal areas. Students repeat this problem with a concave shape. Students...
Lesson Plan
Texas Instruments

Mean Value Theorem

For Teachers 9th - 12th Standards
High schoolers calculate the slopes of secant lines. In this calculus instructional activity, students graph tangent and secant lines using the coordinate plane. They use the Ti calculator to graph and observe the lines.
Worksheet
Curated OER

AP Calculus Practice Exam

For Students 11th - 12th
In this practice exam instructional activity, students solve 17 multiple choice problems. Students find derivatives, points of continuity, maximums, minimums, integrals, and area of enclosed regions.
Worksheet
Curated OER

Intervals

For Students 9th - 12th
For this intervals worksheet, students determine the coordinates at a point of inflection.  They compute the deritative of a function and sketch curves that satisfy given conditions.  Students solve equations using the Mean...
AP Test Prep
College Board

Why We Use Theorem In Calculus

For Teachers 11th - Higher Ed
Young scholars read an article to explain the reasoning behind theorems. In this calculus lesson, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they...
Worksheet
Curated OER

Mean Value Theorem

For Students 12th - Higher Ed
In this Mean Value Theorem, students determine values of a function. They identify the domain, main, maximum and minimum values of a function. This two-page worksheet contains three problems.
Worksheet
Curated OER

Mean Value Theorem - An Application

For Students Higher Ed
In this mean value worksheet, students read a short story problem about driving from one city to another. They use the given information and the mean value theorem to determine why an officer stopped the driver and issued a ticket. ...
Worksheet
Curated OER

Challenge Discussion Sheet 6

For Students 12th - Higher Ed
Students are challenged to determine values that are guaranteed by the mean value theorem. They sketch the graph of a function and show that it satisfies the conditions of the mean value theorem over a given interval. Students determine...
Activity
Mathematics Archives

Math Archives: Visual Calculus: Antiderivatives/average Value of a Function

For Students 9th - 10th
This site has the definition of average of a function by using integrals. The site also contains the proof of the mean value theorem which may be viewed one step at a time. There are links to related exercises whose answer is shown one...
Handout
University of Georgia

University of Georgia: Mean Value Theorem

For Students 9th - 10th
This site has a detailed explanation of the Mean Value Theorem.
Unknown Type
Varsity Tutors

Varsity Tutors: Hotmath: Practice Problems: Applications of Derivatives

For Students 9th - 10th
Hotmath provides 25 practice problems dealing with derivative applications. Each of the practice problems include a step-by-step guide.
Handout
Paul Dawkins

Paul's Online Notes: Average Function Value

For Students 9th - 10th Standards
This tutorial takes a look at using definite integrals to determine the average value of a function on an interval and also the Mean Value Theorem for integrals.
Unit Plan
Mathematics Archives

Math Archives: Visual Calculus: Mean Value Theorem

For Students 9th - 10th
This site provides an explanation as well as formulas and examples of the mean value theorem.
Handout
Harvey Mudd College

Mean Value Theorem: Proof of the Mean Value Theorem

For Students 9th - 10th
A proof of the mean value theorem is offered at this site.
Handout
Texas A&M University

Texas A&m University: Mean Value Theorem

For Students 9th - 10th
Excellent site from the Texas A&M University on The Mean Value Theorem with information on how it relates to the extreme value theorem
Activity
Ministry of Education and Universities of the Region of Murcia (Spain)

Ministerio De Educacion Y Ciencia: Teoremas Del Calculo Diferencial

For Students 9th - 10th
In Spanish. This interactive unit you will be able to analyze the Rolle's Theorem and the Mean Value Theorem of differentiable functions.
Activity
Texas Instruments

Texas Instruments: Mean Value Theorem

For Teachers 9th - 10th
The student will be able to understand the Mean Value Theorem using numerical and graphical methods.
Activity
Paul Dawkins

Paul's Online Notes: Calculus I: Applications of Derivatives

For Students 9th - 10th
Learners examine applications of derivatives. Topics investigated are rates of change, the mean value theorem, optimization problems, critical points, linear approximations, and Newton?s method. Class notes, definitions, and examples...
Activity
Paul Dawkins

Paul's Online Notes: Calculus I: Proofs of Derivative Applications Facts

For Students 9th - 10th
The tutorial consists of proofs of derivative applications. Topics discussed are Fermat?s theorem, mean value theorem, and Rolle?s theorem. Class notes, definitions, and examples with detailed solutions are included. The class notes are...
Activity
Paul Dawkins

Paul's Online Notes: Calculus I: Proof of Various Integral Properties

For Students 9th - 10th
The tutorial examines proofs of several properties of integrals. Topics discussed are the fundamental theorem of calculus, extreme value theorem, work, and mean value theorem. Class notes, proofs, and examples with detailed solutions are...
Activity
Analyze Math

Analyze Math: Mean Value Theorem

For Students 9th - 10th
The interactive applet explores the mean value theorem.
Activity
Analyze Math

Analyze Math: Mean Value Theorem Problems

For Students 9th - 10th
The resource consists of examples with detailed solutions that investigate the mean value theorem.
Handout
Harvey Mudd College

Hmc Mathematics Online Tutorial: The Mean Value Theorem

For Students 9th - 10th
This resource defines the mean value theorem and Rolle's theoem and also discusses key concepts of these theorems.