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Determine the concavity and points of inflection of a function using its second derivative.
Examples
Example: For the graph of the function f(x)=x3-3x, find the points of inflection of f(x) and determine where f(x) is concave upward and concave downward.General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Calculus
Standard: Apply derivatives to solve problems.
Date Adopted or Revised: 08/20
Status: State Board Approved
Related Courses
This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
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Alternate version of this benchmark for students with significant cognitive disabilities.
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Tutorials
Student Resources
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Tutorials
Concavity, concave upwards and concave downwards intervals:
You will learn how to find concavity, concave upwards and concave downwards intervals of functions, and how this relates to the second derivative of a function.
Type: Tutorial
Inflection points of functions:
How to find inflection points of functions graphically and using the second derivaive.
Type: Tutorial
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