Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

AP Calculus AB and BC - Analytical Applications of Differentiation

Krista King via YouTube

Overview

Prepare for a new career with $100 off Coursera Plus
Gear up for jobs in high-demand fields: data analytics, digital marketing, and more.
This course covers Unit 5 of AP Calculus AB and BC, focusing on Analytical Applications of Differentiation. The learning outcomes include understanding concepts such as Mean Value Theorem, Extreme Value Theorem, concavity of functions, optimization problems, and implicit relations. Students will learn how to determine intervals of function behavior, identify extrema, sketch graphs, and solve optimization problems using differentiation techniques. The teaching method includes video lectures, study guides, and practice questions. This course is intended for high school students preparing for the AP Calculus AB and BC exams.

Syllabus

- Introduction.
- 5.1 Using the Mean Value Theorem.
- 5.2 Extreme Value Theorem, Global Versus 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.
- Summary.

Taught by

Krista King

Reviews

Start your review of AP Calculus AB and BC - Analytical Applications of Differentiation

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.