AP®︎ Calculus BC Unit 5: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 5 of AP Calculus BC – 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 BC curriculum.
Using the Mean Value Theorem
Using the Mean Value Theorem
- 1 Using the Mean Value Theorem
- The Mean Value Theorem
- What the Conditions Actually Mean
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 Controls Increasing and Decreasing
- Critical Numbers and Where Behavior Can Change
- The Sign Chart Method
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
- The Process in Action
- Multiplicity and Factored Derivatives
Using the Candidates Test to Determine Absolute (Global) Extrema
Using the Candidates Test to Determine Absolute (Global) Extrema
- What Absolute Extrema Are
- The Candidates Test
- Why Only Critical Points or Endpoints?
Determining Concavity of Functions over Their Domains
Determining Concavity of Functions over Their Domains
- Concavity and the Behavior of the First Derivative
- Using the Second Derivative to Find Intervals of Concavity
- Concavity at a Specific Point
Using the Second Derivative Test to Determine Extrema
Using the Second Derivative Test to Determine Extrema
- What the Second Derivative Test Says
- How to Use the Second Derivative Test
- 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 full graph sketching process
- Moving between \( f \), \( f' \), and \( f'' \)
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
- What Each Derivative Tells You About the Graph
- The Big Structural Connections
Introduction to Optimization Problems
Introduction to Optimization Problems
- What an Optimization Problem Is
- The Optimization Strategy
- Common Optimization Types
Solving Optimization Problems
Solving Optimization Problems
- What an Optimization Problem Is
- The Full Optimization Strategy
- Common Structures of Optimization Problems
Exploring Behaviors of Implicit Relations
Exploring Behaviors of Implicit Relations
- What an Implicit Relation Is and How We Differentiate It
- Critical Points of an Implicit Relation
- Classifying Critical Points Using the First Derivative
Notes
1 credit used · 5/5 remaining