http://www.ck12.org Chapter 3. Applications of Derivatives
3.1 Related Rates
Learning Objectives
A student will be able to:
- Solve problems that involve related rates.
Introduction
In this lesson we will discuss how to solve problems that involve related rates. Related rate problems involve
equations where there is some relationship between two or more derivatives. We solved examples of such equations
when we studied implicit differentiation in Lesson 2.6. In this lesson we will discuss some real-life applications of
these equations and illustrate the strategies one uses for solving such problems.
Let’s start our discussion with some familiar geometric relationships.
Example 1:Pythagorean Theorem
x^2 +y^2 =z^2We could easily attach some real-life situation to this geometric figure. Say for instance thatxandyrepresent the
paths of two people starting at pointpand walking North and West, respectively, for two hours. The quantityz
represents the distance between them at any timet.Let’s now see some relationships between the various rates of
change that we get by implicitly differentiating the original equationx^2 +y^2 =z^2 with respect to timet.