Curated OER
Two Investigations of Cubic Functions
Through learning about cubic functions, high schoolers graph cubic functions on their calculator. Students determine the local maximum and minimum points and the tangent line from the x-intercept to a point on the cubic...
Curated OER
Introduction to Tangent Lines using the TI-Nspire
Students make mathematical argument using the concept of Limit. In this algebra lesson, student calculate the instantaneous rate of change from the linear graph. They use a TI-calculator to create a visual of the graphs.
Curated OER
Limits and Trigonometric Equations.
In this calculus instructional activity, students solve functions dealing with limits and the 6 trigonometric values. They find the slope and tangent lines. There are 28 questions.
Curated OER
Extrema on an Interval
Students explore maximum and minimum points, slopes and tangents. In this Pre-Calculus lesson, students solve optimization problems and find rates of change.
Curated OER
Functions and Differentiation
In this calculus worksheet, students identify functions based on different Theorems as it relates to calculus and the Fundamental Theorem. There are 13 questions dealing with differentiation and trigonometric graphs.
Curated OER
Further Differentiation
In this further differentiation worksheet, students solve and complete 7 various types of problems. First, they sketch the graph of each equation using a stationary point. Then, students find the stationary points of each and describe...
Curated OER
Summer 1999, MA 123: Cumulative Review
In this math learning exercise, students work to complete the review for a final part of an Algebra II class. The sheet has review problems.
Curated OER
A.P. Calculus Exam Prep
In this A.P. Calculus exam practice test, students answer 28 multiple choice questions. Questions cover a wide variety of topics. Students tell the position of a particle moving along a horizontal line. They identify the solution to a...
Curated OER
Find the Average Value of a Function
In this calculus worksheet, 11th graders calculate the average value of a function. They find the line tangent to a curve and graph the equation. There are 15 questions.
Curated OER
Sixteen Multiple Choice AP Calculus BC Exam Preparation Questions
In this review for Calculus BC exam worksheet, students solve sixteen various multiple choice problems. These problems are designed as review and preparation for the AP Calculus Exam.
Curated OER
Converging Series
In this functions worksheet, students calculate the average value, continuity, and the radius of convergence. There are 17 multiple choice questions.
Curated OER
Sixteen Multiple Choice AP Calculus AB Exam Practice Questions
For this AP Calculus AB Exam worksheet, students answer sixteen multiple choice questions in preparation for the AP Exam. These questions include many topics covered on the exam.
Curated OER
Average Value of a Function
In this calculus worksheet, 12th graders calculate the line tangent to a curve and find the average value of a function. There are 12 questions.
Texas Instruments
Texas Instruments: Cubic Inflection
This application of derivatives introduces students to an interesting property of cubics and a method of proving that property using the TI-89 scripts. They then use the CAS of their TI-89 to generalize upon specific results.
Harvey Mudd College
Harvey Mudd College: Concavity and the Second Derivative Test
An excellent tutorial explaining concavity and the second derivative test, including a labeled diagram, examples, and links to a quiz.
Texas Instruments
Texas Instruments: Using Traffic Data to Reinforce Inflection Points in Calculus
Real data from the morning rush on the Chicago expressways is the basis for a piece-wise regression. The students' success depends on their understanding of inflection points. Students need to use the Select command to split the data...
Khan Academy
Khan Academy: Analyzing the Second Derivative to Find Inflection Points
Learn how the second derivative of a function is used in order to find the function's inflection points. Learn which common mistakes to avoid in the process.
CK-12 Foundation
Ck 12: Using the First and Second Derivative Tests
[Free Registration/Login may be required to access all resource tools.] This resource gives a step by step account of how to apply knowledge from First and Second Derivative Tests to sketch graphs of functions. The following table...
Other
Karl's Calculus Tutor: Applications of Derivatives
This detailed site provides five web pages devoted to the various applications of derivatives. Content includes several examples and learning exercises.
Mathematics Archives
Math Archives: Visual Calculus: Graph a Function, Its Second Derivative
This online tutorial site shows that the concavity of a function is related to the second derivative of the function by using an online graphing system. Inflection points are also briefly discussed.
Math Graphs
Houghton Mifflin: Math Graphs: Derivative and Second Derivative [Pdf]
Students use the graph of the derivative to approximate the slope, relative minimum, concavity, and inflection points. The exercise is available in PDF format.
University of California
U of Ca, Davis: Graphing Functions Using Derivatives
Learn about the graphing of functions through useage of the first and second derivatives.
Texas Instruments
Texas Instruments: Quartic Inflection
This activity introduces students to an interesting property of fourth degree polynomials and a method of proving that property using the TI-89 scripts. They then use the CAS of their TI-89 to generalize upon specific results.