Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Derivatives
Subtopic: Related Rate Applications

Overview

Related rate applications occur then the rates of two or more things are being compared in relation to one another. For example, if two vehicles traveling perpendicularly are approaching an intersection, they of course have rates of approach toward the intersection, but at what rate are they approaching each other?

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.12.1 Recognize a real-life situation as a related rate application
• 2.12.2 When setting-up a related rate problem, know to which variable you should differentiate with respect to
• 2.12.3 When setting-up a related rate problem, establish which rates are given and which rate is to be found
• 2.12.4 Translate a related rate application problem into a differential equation
• 2.12.5 Solve a related rate application problem using proper mathematical notation and format
• 2.12.6 Interpret the result of an optimization application problem including recognizing the reasonableness of the answer
• 2.12.7 Understand classic calculus related rate problems including those that use similar triangles to set-up the differential equation(s).
• 2.12.8 Demonstrate an understanding of the connections between the equations, process, and graphical representations in a related rate application problem.

Terminology

Terms you should be able to define: related rates, differentiating with respect to time

Mini-Lectures and Examples

Supplemental Resources (optional)

rev. 2020-10-31