Chapter 2, Problem 1RE

These review exercises are for test preparation. They can also be used as a practice test. Answers are at the back of the book. The red bracketed section references tell you what part(s) of the chapter to restudy if your answer is incorrect.

Concept Reinforcement

Match each description in column A with the most appropriate graph in column B.

Column A	Column B
A function with a relative maximum but no absolute extrema

To determine

The graph from the provided graph that matches thestatement “A function with a relative maximum but no absolute extrema”.

Answer to Problem 1RE

Solution:

The graph that matches the provided statement is, (g) and is shown below,

Explanation of Solution

Given Information:

The statement, “A function with a relative maximum but no absolute extrema” and the graphs to choose the correct one.

Consider the provided statement:

“A function with a relative maximum but no absolute extrema.”

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained.

A localextremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function is obtained in some  open interval containing the point.

An absolute extremum (or global extremum) of a function is the point at which a maximum or minimum value of the function is obtainedin the interval on which the function is defined.

We can see that the graph of the function given below has a relative maximum but no absolute maximum.

Hence, the graph that matches the provided statement is (g).