Created on: September 5, 2008

Website Address: https://library.curriki.org/oer/MIT-OpenCourseWare--AP-Calculus--Second-Derivatives

TABLE OF CONTENTS

- MIT - Chemistry Laboratory Techniques
- MIT OpenCoruseWare - AP Physics - Kinematics
- MIT OpenCourseWare - AP Biology - Cells
- MIT OpenCourseWare - AP Biology - Heredity
- MIT OpenCourseWare - AP Biology - Ecology
- MIT OpenCourseWare - AP Physics - Electrostatics
- MIT OpenCourseWare - AP Physics - Electromagnetism
- MIT OpenCourseWare - AP Physics - Waves
- MIT OpenCourseWare - AP Biology - Chemistry of Life
- MIT OpenCourseWare - AP Physics - Kinetic Theory/Thermodynamics
- MIT OpenCourseWare - AP Physics - Geometric Optics
- MIT OpenCourseWare - AP Calculus - Analysis of Graphs
- MIT OpenCourseWare - AP Biology - Cellular Energetics
- MIT OpenCourseWare - AP Biology - Molecular Genetics
- MIT OpenCourseWare - AP Biology - Evolutionary Biology
- MIT OpenCourseWare - AP Biology - Diversity of Organisms
- MIT OpenCourseWare - AP Calculus - Limits of Functions
- MIT OpenCourseWare - AP Calculus - Second Derivatives
- MIT OpenCourseWare - AP Calculus - Applications of Derivatives
- MIT OpenCourseWare - AP Calculus - Computation of Derivatives
- MIT OpenCourseWare - AP Calculus - Applications of Integrals
- MIT OpenCourseWare - AP Calculus - Antidifferentiation Techniques
- MIT OpenCourseWare - AP Calculus - Applications of Antidifferentiation
- MIT OpenCourseWare - AP Calculus - Concept of Series
- MIT OpenCourseWare - AP Calculus - Series of Constants
- MIT OpenCourseWare - AP Calculus - Computation of Derivatives
- MIT OpenCourseWare - AP Physics - Work, Energy, Power
- MIT OpenCourseWare - AP Physics - Circular Motion & Rotation
- MIT OpenCourseWare - AP Physics - Oscillations & Gravitation
- MIT OpenCourseWare - AP Physics - Fluid Mechanics
- MIT OpenCourseWare - AP Physics - Temperature & Heat
- MIT OpenCourseWare - AP Physics - Conductors, Capacitors, Dielectrics
- MIT OpenCourseWare - AP Physics - Electric Circuits
- MIT OpenCourseWare - AP Physics - Magnetic Fields
- MIT OpenCourseWare - AP Physics - Physical Optics
- MIT OpenCourseWare - AP Physics - Atomic Physics & Quantum Effects
- MIT OpenCourse Ware - AP Calculus - Asymptotic & Unbounded Behavior
- MIT OpenCourseWare - AP Calculus - Continuity: Property of Functions
- MIT OpenCourseWare - AP Calculus - Parametric, Polar & Vector Functions
- MIT OpenCourseWare - AP Calculus - Parametric, Polar & Vector Functions
- MIT OpenCourseWare - AP Calculus - Concept of the Derivative
- MIT OpenCourseWare - AP Calculus - Derivative at a Point
- MIT OpenCourseWare - AP Calculus - Derivative as a Function
- MIT OpenCourseWare - AP Calculus - Fundamental Theorem of Calculus
- MIT OpenCourseWare - AP Physics - Newton's Laws of Motion
- MIT OpenCourseWare - AP Biology - Structure & Function of Plants & Animals
- MIT OpenCourseWare - AP Calculus - Interpretations & Properties of Definite Integrals
- MIT OpenCourseWare - AP Calculus - Numerical Approximations to Definite Integrals
- MIT OpenCourseWare - AP Physics - Systems of Particles, Linear Momentum

We have selected relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP® Calculus curriculum. These do not comprise a full course of study but offer material to supplement the understanding of the AP Calculus curriculum.

Second Derivatives covers the topics of characteristics: graphs of f, f' & f''; the relationship between concavity of f and sign of f''; and points of inflection and concavity changes using a mixture of lecture notes and exam questions.

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc

http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

<

The lecture notes contained in this section of the AP Calculus materials cover the characteristics of graphs of f, f’, and f”. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes contained in this section of the AP Calculus materials cover the relationship between behavior of f & sign of f’. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes contained in this section of the AP Calculus materials cover points of inflection and concavity changes. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode