First Derivative Test
Definition
The First Derivative Test is a method used to determine the intervals on which a function is increasing or decreasing, and to identify local extrema (maximum or minimum) points.
Related terms
Critical Points: These are the points where the derivative of a function equals zero or does not exist.
Local Extrema: These are the maximum and minimum points of a function within a specific interval.
Increasing/Decreasing Intervals: These are intervals where the function is either always increasing or always decreasing.
"First Derivative Test" appears in:
Study guides (3)
AP Calculus AB/BC - 5.3 Determining Intervals on Which a Function is Increasing or Decreasing
AP Calculus AB/BC - 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
AP Calculus AB/BC - 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
Additional resources (1)
AP Calculus AB/BC - 2024 AP Calculus AB Exam Guide
Practice Questions (7)
What does the first derivative test help determine about a critical point?
What is the First Derivative Test used for?
How can you determine the intervals on which a function is increasing or decreasing using the First Derivative Test?
How does the First Derivative Test help determine local extrema?
How can you determine the intervals of concavity for a function using the First Derivative Test?
What is the purpose of the First Derivative Test in calculus?
What is the purpose of graphing the function when using the First Derivative Test?
Are you a college student?
Study guides for the entire semester
200k practice questions
Glossary of 50k key terms - memorize important vocab
About Us
About Fiveable
Blog
Careers
Code of Conduct
Terms of Use
Privacy Policy
CCPA Privacy Policy
Resources
Cram Mode
AP Score Calculators
Study Guides
Practice Quizzes
Glossary
Cram Events
Merch Shop
Crisis Text Line
Help Center
Stay Connected
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
About Us
About Fiveable
Blog
Careers
Code of Conduct
Terms of Use
Privacy Policy
CCPA Privacy Policy
Resources
Cram Mode
AP Score Calculators
Study Guides
Practice Quizzes
Glossary
Cram Events
Merch Shop
Crisis Text Line
Help Center
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.