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ap calc - derivatives & graphs

originally streamed in 2020 with Meghan DwyerTeacher
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Understand how derivatives connect to graphs and learn to analyze function behavior in AP Calculus. This video walks you through reading derivative graphs, finding critical points, and interpreting what f(x), f'(x), and f''(x) reveal about curves. Y ...more

covered in this stream

units
Unit 2 – Fundamentals of DifferentiationUnit 3 – Composite, Implicit, and Inverse FunctionsUnit 4 – Contextual Applications of DifferentiationUnit 5 – Analytical Applications of Differentiation
topics
2.1 Defining Average and Instantaneous Rates of Change at a Point2.2 Defining the Derivative of a Function and Using Derivative Notation2.8 The Product Rule2.9 The Quotient Rule3.1 The Chain Rule4.1 Interpreting the Meaning of the Derivative in Context5.1 Using the Mean Value Theorem5.3 Determining Intervals on Which a Function is Increasing or Decreasing5.4 Using the First Derivative Test to Determine Relative (Local) Extrema5.6 Determining Concavity5.8 Sketching Graphs of Functions and Their Derivatives5.9 Connecting a Function, Its First Derivative, and its Second Derivative

timestamps

  • 0:00

    Introduction and Setup

  • 0:38

    PowerPoint Overview

  • 1:48

    Agenda and Resources

  • 2:19

    Meaning of Derivative Review

  • 3:22

    Derivative Definitions

  • 3:52

    Limit Definition Explained

  • 5:58

    Derivative Notations

  • 7:35

    Graphs of Functions and Derivatives

  • 9:38

    Positive Slope and Increasing Functions

  • 11:14

    Second Derivative and Concavity

  • 13:50

    Maxima and Minima Analysis

  • 15:23

    Units of Measurement

  • 17:01

    Mean Value Theorem

  • 20:10

    Truck Velocity Problem

  • 25:22

    MVT Application Check

  • 28:58

    Derivative Rules Overview

  • 30:03

    Tangent Line to g(x)

  • 35:49

    Quotient and Chain Variations

  • 39:59

    h(x) Composition Problem

  • 44:41

    k(x) Product Analysis

  • 48:19

    Intervals and Extrema

  • 52:58

    Lesson Review and Closing

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history

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social science

āœŠšŸæ ap african american studiesšŸ—³ļø ap comparative government🚜 ap human geographyšŸ’¶ ap macroeconomicsšŸ¤‘ ap microeconomics🧠 ap psychologyšŸ‘©šŸ¾ā€āš–ļø ap us government

english & capstone

āœšŸ½ ap english languagešŸ“š ap english literaturešŸ” ap researchšŸ’¬ ap seminar

arts

šŸŽØ ap art & designšŸ–¼ļø ap art historyšŸŽµ ap music theory

science

🧬 ap biology🧪 ap chemistryā™»ļø ap environmental sciencešŸŽ” ap physics 1🧲 ap physics 2šŸ’” ap physics c: e&māš™ļø ap physics c: mechanics

math & computer science

🧮 ap calculus abā™¾ļø ap calculus bcšŸ“ ap precalculusšŸ“Š ap statisticsšŸ’» ap computer science aāŒØļø ap computer science p

world languages

šŸ‡ØšŸ‡³ ap chinesešŸ‡«šŸ‡· ap frenchšŸ‡©šŸ‡Ŗ ap germanšŸ‡®šŸ‡¹ ap italianšŸ‡ÆšŸ‡µ ap japanesešŸ›ļø ap latinšŸ‡ŖšŸ‡ø ap spanish languagešŸ’ƒšŸ½ ap spanish literature

go beyond AP

high school exams

āœļø PSATšŸŽ“ Digital SATšŸŽ’ ACT

honors classes

šŸ¬ honors algebra IIšŸ«€ honors anatomyšŸ‡ honors biologyšŸ‘©šŸ½ā€šŸ”¬ honors chemistryšŸ’² honors economicsšŸ“ honors geometryāš¾ļø honors physicsšŸ“ honors pre-calculusšŸ“Š honors statisticsšŸ—³ļø honors us governmentšŸ‡ŗšŸ‡ø honors us historyšŸŒŽ honors world history

college classes

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hs classes

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APĀ® and SATĀ® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.