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Find points of inflection of functions. Understand the relationship between the concavity of f and the sign of f". Understand points of inflection as places where concavity changes.
Remarks
Example: For the graph of the function
, find the points of inflection of f(x) and determine where f(x) is concave upward and concave downward.
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Applications of Derivatives - Apply knowledge about derivatives to find slopes of curves and the related tangent lines. Analyze and graph functions, finding where they are increasing or decreasing, their maximum and minimum points, their points of inflection, and their concavity. Solve optimization problems, find average and instantaneous rates of change (including velocities and accelerations), and model rates of change. Find slopes and equations of tangent lines, maximum and minimum points, and points of inflection. Solve optimization problems, and find rates of change.
Date Adopted or Revised: 02/14
Content Complexity Rating:
Level 2: Basic Application of Skills & Concepts
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More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Related Courses
This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
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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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