# MA.912.C.3.5

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.)
Strand: Calculus
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))

## 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

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

Recognizing Concavity of Functions:

Learn how to recognizing concavity of functions.

Type: Tutorial

Inflection points of functions:

How to find inflection points of functions graphically and using the second derivaive.

Type: Tutorial

## 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

Recognizing Concavity of Functions:

Learn how to recognizing concavity of functions.

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.