5 Steps to a 5 AP Calculus BC 2019

CHAPTER 8

Big Idea 2: Derivatives

Applications of Derivatives

IN THIS CHAPTER

Summary:Two of the most common applications of derivatives involve solving

related rate problems and applied maximum and minimum problems. In this chapter,

you will learn the general procedures for solving these two types of problems and to

apply these procedures to examples. Both related rate and applied maximum and

minimum problems appear often on the AP Calculus BC exam.

Key Ideas

KEY IDEA !General Procedure for Solving Related Rate Problems

!Common Related Rate Problems

!Inverted Cone, Shadow, and Angle of Elevation Problems

!General Procedure for Solving Applied Maximum and Minimum Problems

!Distance, Area, Volume, and Business Problems

8.1 Related Rate

Main Concepts:General Procedure for Solving Related Rate Problems, Common

Related Rate Problems, Inverted Cone (Water Tank) Problem,

Shadow Problem, Angle of Elevation Problem

STRATEGY

General Procedure for Solving Related Rate Problems

1. Read the problem and, if appropriate, draw a diagram.


2. Represent the given information and the unknowns by mathematical symbols.


3. Write an equation involving the rate of change to be determined. (If the equation con-
   tains more than one variable, it may be necessary to reduce the equation to one variable.)

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