The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

How to Set Up a Problem

In applications, a calculus problem is often presented verbally, and it is up to you to set up the problem in mathematical terms. The problem can usually be described mathematically by a list of equations and inequalities. The next two sections contain several examples that illustrate the process of setting up a problem. The examples in this section are from algebra and geometry, and those in the next section are from calculus.

It is sometimes hard to see how to begin on a story problem. It is helpful to break the process up into three steps:

Step 1

Draw a diagram if possible, and label all quantities involved.

Step 2

Write the given information as a set of equations and/or inequalities.

Step 3

Solve the mathematical problem, and interpret the mathematical solution to answer the original story problem.

Last Update: 2006-11-25