# Cartesian Graphs and the Second Derivative

Taught by TheMathDude
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Lesson Summary:

In this lesson, the instructor explains how to analyze and interpret Cartesian graphs in terms of the second derivative, which relates to acceleration and deceleration based on inflection points and concavity. Using examples and graphs, the instructor demonstrates how to distinguish regions of acceleration from regions of deceleration by looking at the concavity and inflection points in the original function. The lesson also covers how to numerically find the coordinates of an inflection point by using technology such as calculators or Wolfram Alpha.

Lesson Description:

Be able to analyze and interpret Cartesian graphs of a function in terms of the second derivative (i.e. acceleration or deceleration based on inflection points and concavity).

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• How do you analyze and interpret the Cartesian graph of a function in terms of its second derivative?
• What is an inflection point of a graph?
• What are acceleration and deceleration of a function?
• How can you tell from the second derivative of a function where the function is accelerating and decelerating?
• What does the second derivative of a function tell you?
• How can you find the location of an inflection point of a function from its second derivative?
• How can you take the numerical derivative of a function on a TI graphing calculator?
• How can you graph a function and its derivative on a TI graphing calculator?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson shows you the second derivative of a function and takes some information from this second derivative to learn something about the original function. This is a great tutorial on learning concepts from the second derivative of a function. Two different functions and their derivatives and second derivatives are examined.