AP®︎ Calculus AB Unit 5: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 5 of AP Calculus AB – Analytical Applications of Differentiation.
Unit 5: Analytical Applications of Differentiation
Analyze functions using derivatives and solve optimization and graph-analysis problems.
Begin with Topic 5.1: Using the Mean Value Theo...To review Unit 5, go through each of the 12 topics below.
Everything you actually need to know for your Unit 5 test, pulled directly from the AP® Calculus AB curriculum.
Using the Mean Value Theorem
Using the Mean Value Theorem
- The Mean Value Theorem
- The Two Conditions You Must Check
- Using MVT to Justify a Derivative Value Exists
Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- The Extreme Value Theorem
- Global vs Local Extrema
- Critical Points
Determining Intervals on Which a Function Is Increasing or Decreasing
Determining Intervals on Which a Function Is Increasing or Decreasing
- How the First Derivative Determines Increasing and Decreasing
- Where a Function Can Change Behavior
- The Process for Finding Increasing and Decreasing Intervals
Using the First Derivative Test to Determine Relative (Local) Extrema
Using the First Derivative Test to Determine Relative (Local) Extrema
- What the First Derivative Test Says About Local Extrema
- The Full Classification at a Critical Point
- How to Apply the First Derivative Test
Using the Candidates Test to Determine Absolute (Global) Extrema
Using the Candidates Test to Determine Absolute (Global) Extrema
- Absolute Extrema on a Closed Interval
- Why Only Critical Points and Endpoints?
- The Candidates Test
Determining Concavity of Functions over Their Domains
Determining Concavity of Functions over Their Domains
- What Concavity Means
- The Second Derivative
- Finding Intervals of Concavity
Using the Second Derivative Test to Determine Extrema
Using the Second Derivative Test to Determine Extrema
- The Second Derivative Test
- The Full Procedure
- When the Test Is Inconclusive
Sketching Graphs of Functions and Their Derivatives
Sketching Graphs of Functions and Their Derivatives
- How Derivatives Determine the Shape of a Graph
- The Complete Graph Sketching Checklist
- First vs Second Derivative Tests
Connecting a Function, Its First Derivative, and Its Second Derivative
Connecting a Function, Its First Derivative, and Its Second Derivative
- How f, f′, and f'' Are Connected
- Increasing, Decreasing, and Relative Extrema
- Concavity and Points of Inflection
Introduction to Optimization Problems
Introduction to Optimization Problems
- What an Optimization Problem Is
- The Optimization Strategy
- Common Optimization Setups
Solving Optimization Problems
Solving Optimization Problems
- What an Optimization Problem Is
- The Core Structure of Every Optimization Problem
- The Optimization Process in Action
Exploring Behaviors of Implicit Relations
Exploring Behaviors of Implicit Relations
- Implicit Relations and Their Derivatives
- Critical Points of an Implicit Relation
- Using the First Derivative to Describe Behavior
Notes
1 credit used · 5/5 remaining