Unit 05 - Analytical Applications of Differentiation

Concept Index

TheoremsShape of a CurveOptimizationMisc.

• 5.1 Using the Mean Value Theorem
• 5.2 Extreme Value Theorem, Global vs. Local Extrema, and Critical Points

• 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
• 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
• 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
• 5.6 Determining Concavity of Functions over Their Domains
• 5.7 Using the Second Derivative Test to Determine Extrema
• 5.8 Sketching Graphs of Functions and Their Derivatives
• 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

• 5.10 Introduction to Optimization Problems
• 5.11 Solving Optimization Problems

• 5.12 Exploring Behaviors of Implicit Relations