College Board
Differentiability of Piecewise Defined Functions
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®...
Curated OER
Worksheet 15-Fall 1995
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...
Texas Instruments
Mean Value Theorem
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.
Curated OER
AP Calculus Practice Exam
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.
Curated OER
Intervals
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...
College Board
Why We Use Theorem In Calculus
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...
Curated OER
Mean Value Theorem
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.
Curated OER
Mean Value Theorem - An Application
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. ...
Curated OER
Challenge Discussion Sheet 6
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...
Mathematics Archives
Math Archives: Visual Calculus: Antiderivatives/average Value of a Function
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...
University of Georgia
University of Georgia: Mean Value Theorem
This site has a detailed explanation of the Mean Value Theorem.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Applications of Derivatives
Hotmath provides 25 practice problems dealing with derivative applications. Each of the practice problems include a step-by-step guide.
Paul Dawkins
Paul's Online Notes: Average Function Value
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.
Mathematics Archives
Math Archives: Visual Calculus: Mean Value Theorem
This site provides an explanation as well as formulas and examples of the mean value theorem.
Harvey Mudd College
Mean Value Theorem: Proof of the Mean Value Theorem
A proof of the mean value theorem is offered at this site.
Texas A&M University
Texas A&m University: Mean Value Theorem
Excellent site from the Texas A&M University on The Mean Value Theorem with information on how it relates to the extreme value theorem
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Teoremas Del Calculo Diferencial
In Spanish. This interactive unit you will be able to analyze the Rolle's Theorem and the Mean Value Theorem of differentiable functions.
Texas Instruments
Texas Instruments: Mean Value Theorem
The student will be able to understand the Mean Value Theorem using numerical and graphical methods.
Paul Dawkins
Paul's Online Notes: Calculus I: Applications of Derivatives
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...
Paul Dawkins
Paul's Online Notes: Calculus I: Proofs of Derivative Applications Facts
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...
Paul Dawkins
Paul's Online Notes: Calculus I: Proof of Various Integral Properties
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...
Analyze Math
Analyze Math: Mean Value Theorem
The interactive applet explores the mean value theorem.
Analyze Math
Analyze Math: Mean Value Theorem Problems
The resource consists of examples with detailed solutions that investigate the mean value theorem.
Harvey Mudd College
Hmc Mathematics Online Tutorial: The Mean Value Theorem
This resource defines the mean value theorem and Rolle's theoem and also discusses key concepts of these theorems.