Word (.docx)
Acrobat (.pdf)
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 - 2024, 2024 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
Tutorials
Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
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
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
