Page 14 - How To Solve Word Problems In Calculus

Chapter 1

Extracting Functions from

Word Problems

Calculus is the study of the behavior of functions. The ability to
solve “real life” problems using calculus hinges upon the abi-
lity to extract a function from a given description or physical
situation.
Students usually find that a word problem is easily solved
once the underlying mathematical function is determined. In
this chapter we discuss techniques that will form the basis for
solving a variety of word problems encountered in calculus
courses.
One definition of a function found in calculus texts reads:

A function is a rule that assigns to each number x ε A,a
unique number y ε B.

In calculus, A and B are sets of real numbers. A is called the
domain and B the range. It is important to understand that a
function is not a number, but a correspondence between two
sets of numbers. In a practical sense, one may think of a func-
tion as a relationship between y and x. The important thing
is that there be one, and only one, value of y corresponding to
a given value of x.

EXAMPLE 1
2
If y = x + 5x + 2, then y is a function of x. For each value of
x there is clearly one and only one value of y. However, if the

1

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