Intermediate Value Theorem


In this intermediate value theorem instructional activity, 11th graders solve and complete 7 different types of problems. First, they sketch the graph of each function for the indicated values. Then, students use the intermediate value theorem to show that the function has a zero between each given variable.

Resource Details

Algebra II

Mean Value Theorem and Rolle's Theorem

This Mean Value Theorem and Rolle's Theorem worksheet is very thorough in explaining the two Theorums and showing the formulas.  There are six prractice problems for classwork, and eight additional problems for homework.

Absolute Value of Linear Functions

Students discover how abolute value affects linear functions. They complete a worksheet simulating a path for miniature golf hole in one for three figures. They construct a hole in one graph for each hole marking the X and Y coordinates.

Somewhere in the Middle

Students explore the concept of the mean value theorem.  Students use their Ti-Nspire to explore the mean value theorem using secant and tangent lines.  Students find the derivatives of functions like x^2 or sin x.

Mean Value Theorem

In this mean value theorem worksheet, students solve and complete 8 various types of problems. First, they sketch the graph of a function and find all local and absolute extrema on the interval given. Then, students find the critical numbers of each function. They also find the absolute maximum and minimum values for each function.


For this intervals worksheet, learners 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 Value Theorem and Rolle's Theorem for given functions.  This seven-page worksheet contains 20 multi-step problems.

Average Roller Coaster

Students explore the concept of average value of a function.  In this average value of a function lesson, students use their Ti-Nspire to determine the average value of a quadratic function.  Students take the integrals of velocity functions using trapezoids.

Function Inverses Example 1

Sal continues looking at function inverses in this video by showing two examples. In each example, he finds the inverse and shows the graph of both functions. Both of his examples are with linear functions, but his first example shows a function whose inverse is the same as the function. You might consider having students find the inverse of such a function and see if they can determine why its inverse is the same and why it make sense, before you have them watch this video.

Introduction to Function Inverses

Starting from a brief look at functions and the mapping of domains to ranges, Sal starts out with an intuitive sense of what a function inverse is. He then, using an example, shows how to find the inverse of a function and also shows how the graph of the function and its inverse are reflections over the y = x line. This video provides a good review of function inverses for more advanced students or a nice introduction for the beginning student.

Mean Value Theorem

Sal spends most this video explaining what the Mean Value Theorem says in a very intuitive way. He follows this with a concrete example of finding the value of a function on a closed interval where the slope is the same as the average slope of the function over that interval. Here, Sal also uses and informally defines the terms: continuous function, differential, and closed and open interval.

MVT for Derivatives

Young scholars find the derivative using the mean value theorem in this calculus lesson. They find the slopes of secant and tangent lines, then analyze the function and identify the slope.

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