BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 3RQ
To determine

Whether the statement, if f is continuous on (a,b) then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in (a,b) is true or false.

Expert Solution

Explanation of Solution

The given statement is false.

Reason:

Case 1:

If the graph of the function is a line parallel to x-axis, then there will be no absolute minimum or an absolute maximum.

Case 2:

If the graph of the function is a line which is defined on any open interval (a, b), then there will be no absolute minimum or an absolute maximum.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 3RQ

From Figure 1, it can be identified that either the horizontal line or a straight line does not attain its absolute minimum or absolute maximum.

Therefore, the given statement is false.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!