free diagnosticupgrade
  1. browse cram archives
  2. ap calculus ab/bc
  3. AP Calc - Concavity & Inflection Points

ap calc - concavity & inflection points

originally streamed in 2020 with Sander OwensStudent
subscribe
Learn how concavity and inflection points work in AP Calculus using the second derivative test. This video breaks down concave up vs. concave down intervals, shows you how to find inflection points, and connects these concepts to function behavior—al ...more

covered in this stream

units
Unit 5 – Analytical Applications of Differentiation
topics
5.6 Determining Concavity5.7 Using the Second Derivative Test to Determine Extrema5.9 Connecting a Function, Its First Derivative, and its Second Derivative 5.8 Sketching Graphs of Functions and Their Derivativesf, f', f''5.3 Determining Intervals on Which a Function is Increasing or Decreasing5.4 Using the First Derivative Test to Determine Relative (Local) Extrema5.2 Extreme Value Theorem, Global vs Local Extrema, and Critical Points

timestamps

  • 0:00

    Introduction and Stream Overview

  • 0:31

    Social Media and Subjects

  • 1:03

    Reviewing f, f', f''

  • 2:36

    Finding Derivatives

  • 3:38

    Derivative Notation Explained

  • 5:12

    Derivative Rules Review

  • 8:50

    Practice Finding Derivatives

  • 11:55

    What f' Tells You

  • 13:28

    Sign Charts and Graphs

  • 15:32

    What f'' Tells You

  • 17:06

    Concavity and Inflection Points

  • 18:38

    Determining Extrema

  • 21:15

    Defining Concavity

  • 23:18

    Second Derivative Test

  • 26:28

    Graphical Examples

  • 31:43

    Inflection Points Analysis

  • 33:50

    Concavity in Straight Lines

  • 36:28

    Algebraic Examples

  • 40:05

    Concave Up Intervals

  • 41:39

    Sine Function Concavity

  • 45:13

    Given f' Concave Up

  • 46:50

    Always Concave Cases

  • 47:52

    Physics Interpretation

  • 49:56

    Physics Examples

  • 51:59

    Summary Table

  • 54:05

    AP Exam Advice

  • 56:08

    Closing and Thanks

more on these topics
AP Calc CRAM – Curve Sketching

1:15:48

AP Calc CRAM – Curve Sketching

2020 · Jamil Siddiqui

AP Calc AB - Derivative Graph FRQs

1:38:00

AP Calc AB - Derivative Graph FRQs

2020 · Bob Amar

AP Calculus - Connecting f, f', and f'' Graphs

51:19

AP Calculus - Connecting f, f', and f'' Graphs

2019 · Jenni Durost

AP Calculus - Mid-Year Review: Limits & Derivatives

1:20:11

AP Calculus - Mid-Year Review: Limits & Derivatives

2019 · Jenni Durost

AP Calculus AB - Q&A: Theorems, Derivatives & Integrals

46:26

AP Calculus AB - Q&A: Theorems, Derivatives & Integrals

2019 · Brandon Wu

up next in ap calculus ab/bc
AP Calculus - Preview Session: Exam Prep & Study Tips

1:02:22

AP Calculus - Preview Session: Exam Prep & Study Tips

2024 · Jude St John

AP Calculus CRAM – Related Rates & Implicit Differentiation

5:00:44

AP Calculus CRAM – Related Rates & Implicit Differentiation

2020

AP Calculus - Q&A: Differential Equations & Slope Fields

1:09:44

AP Calculus - Q&A: Differential Equations & Slope Fields

2020 · Leen & Jacob

AP Calculus CRAM – Separable Differential Equations

1:06:12

AP Calculus CRAM – Separable Differential Equations

2020

AP Calculus AB - Interpreting Derivatives & Integrals

1:00:39

AP Calculus AB - Interpreting Derivatives & Integrals

2020 · Meghan Dwyer

more from Sander Owens
AP Statistics - Q&A: Two-Variable Data & Regression

37:11

AP Statistics - Q&A: Two-Variable Data & Regression

2020 · Sander Owens

AP Statistics - Unit 1 Q&A: Data Analysis & Distributions

35:48

AP Statistics - Unit 1 Q&A: Data Analysis & Distributions

2020 · Sander Owens

AP Calculus - Derivative Rules Practice

48:06

AP Calculus - Derivative Rules Practice

2019 · Sander Owens

AP Calculus - Derivative Rules Practice

58:10

AP Calculus - Derivative Rules Practice

2019 · Sander Owens

AP Statistics - FRQ Practice: Regression & Distribution

31:45

AP Statistics - FRQ Practice: Regression & Distribution

2019 · Sander Owens

Fiveable

Study Content & Tools

Study GuidesFRQs + AI ScoringAP Essay Grader for StudentsAI Grading for TeachersPractice QuestionsGlossaryScore Calculators

Company

What's New?PricingBulk DiscountsTestimonialsFAQsEmail us

Resources

AP Exam Schedule 2027AP ClassesAP ClassroomEasiest AP ClassesHardest AP ClassesAP vs IBAP vs Dual EnrollmentAP vs Honors ClassesAP Scholar Awards

every AP exam is fiveable

history

🌎 ap world history🇺🇸 ap us history🇪🇺 ap european history

social science

✊🏿 ap african american studies🗳️ ap comparative government🚜 ap human geography💶 ap macroeconomics🤑 ap microeconomics🧠 ap psychology👩🏾‍⚖️ ap us government

english & capstone

✍🏽 ap english language📚 ap english literature🔍 ap research💬 ap seminar

arts

🎨 ap art & design🖼️ ap art history🎵 ap music theory

science

🧬 ap biology🧪 ap chemistry♻️ ap environmental science🎡 ap physics 1🧲 ap physics 2💡 ap physics c: e&m⚙️ ap physics c: mechanics

math & computer science

🧮 ap calculus ab♾️ ap calculus bc📐 ap precalculus📊 ap statistics💻 ap computer science a⌨️ ap computer science p

world languages

🇨🇳 ap chinese🇫🇷 ap french🇩🇪 ap german🇮🇹 ap italian🇯🇵 ap japanese🏛️ ap latin🇪🇸 ap spanish language💃🏽 ap spanish literature

go beyond AP

high school exams

✏️ PSAT🎓 Digital SAT🎒 ACT

honors classes

🍬 honors algebra II🫀 honors anatomy🐇 honors biology👩🏽‍🔬 honors chemistry💲 honors economics📐 honors geometry⚾️ honors physics📏 honors pre-calculus📊 honors statistics🗳️ honors us government🇺🇸 honors us history🌎 honors world history

college classes

👩🏽‍🎤 arts👔 business🎤 communications🏗️ engineering📓 humanities➗ math🧑🏽‍🔬 science💶 social science

hs classes

🏛️ alabama history⛰️ appalachian studies🌴 california history🌍 earth science🌐 ethnic studies🐊 florida history🍑 georgia history🌎 global studies🌺 hawaiian studies📰 journalism🪶 native american studies🌵 new mexico history🤠 oklahoma history⚗️ physical science🎙️ speech and debate🤝 texas government🤠 texas history🌲 washington state history🕊️ world religions

RefundsTermsPrivacyCCPAAI TransparencySchool Data Privacy

© 2026 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.

every AP exam is fiveable

Fiveable

Study Content & Tools

Study GuidesFRQs + AI ScoringAP Essay Grader for StudentsAI Grading for TeachersPractice QuestionsGlossaryScore Calculators

Company

What's New?PricingBulk DiscountsTestimonialsFAQsEmail us

Resources

AP Exam Schedule 2027AP ClassesAP ClassroomEasiest AP ClassesHardest AP ClassesAP vs IBAP vs Dual EnrollmentAP vs Honors ClassesAP Scholar Awards

history

🌎 ap world history🇺🇸 ap us history🇪🇺 ap european history

social science

✊🏿 ap african american studies🗳️ ap comparative government🚜 ap human geography💶 ap macroeconomics🤑 ap microeconomics🧠 ap psychology👩🏾‍⚖️ ap us government

english & capstone

✍🏽 ap english language📚 ap english literature🔍 ap research💬 ap seminar

arts

🎨 ap art & design🖼️ ap art history🎵 ap music theory

science

🧬 ap biology🧪 ap chemistry♻️ ap environmental science🎡 ap physics 1🧲 ap physics 2💡 ap physics c: e&m⚙️ ap physics c: mechanics

math & computer science

🧮 ap calculus ab♾️ ap calculus bc📐 ap precalculus📊 ap statistics💻 ap computer science a⌨️ ap computer science p

world languages

🇨🇳 ap chinese🇫🇷 ap french🇩🇪 ap german🇮🇹 ap italian🇯🇵 ap japanese🏛️ ap latin🇪🇸 ap spanish language💃🏽 ap spanish literature

go beyond AP

high school exams

✏️ PSAT🎓 Digital SAT🎒 ACT

honors classes

🍬 honors algebra II🫀 honors anatomy🐇 honors biology👩🏽‍🔬 honors chemistry💲 honors economics📐 honors geometry⚾️ honors physics📏 honors pre-calculus📊 honors statistics🗳️ honors us government🇺🇸 honors us history🌎 honors world history

college classes

👩🏽‍🎤 arts👔 business🎤 communications🏗️ engineering📓 humanities➗ math🧑🏽‍🔬 science💶 social science

hs classes

🏛️ alabama history⛰️ appalachian studies🌴 california history🌍 earth science🌐 ethnic studies🐊 florida history🍑 georgia history🌎 global studies🌺 hawaiian studies📰 journalism🪶 native american studies🌵 new mexico history🤠 oklahoma history⚗️ physical science🎙️ speech and debate🤝 texas government🤠 texas history🌲 washington state history🕊️ world religions
RefundsTermsPrivacyCCPAAI TransparencySchool Data Privacy

© 2026 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.