Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q 49. (page 90)

In Problems 45–52, for each graph of a function y=f(x), find the absolute maximum and the absolute minimum, if they exist.

Short Answer

Expert verified

The absolute minimum is 0 and the function has no absolute maximum.

Step by step solution

01

Step 1. Given information. 

The given graph of the function y=f(x)is:

02

Step 2. Use the concept of absolute maximum and absolute minimum.

Let fdenote a function defined on some interval I. If there is a number u in I for whichf(x)≤f(u) for all x in I, thenf(u) is the absolute maximum of f and I.

If there is a number v in I for which f(x)≤f(v) for all x in I , then f(v)is the absolute minimum of f on I.

03

Step 3. Find the absolute maximum.

We can see from the graph that the given function has the domain {x-1≤x<4}.

The function is approaching infinity at point x=4.

Thus, the largest value of fis not defined.

The function has no absolute maximum value.

04

Step 4. Find the absolute minimum.

We can see from the graph that the given function has a minimum value at its domain is:

f(0)=0

The smallest value of fisf(0)=0.

Therefore, the absolute minimum of the function is 0.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.

match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

If 3,6is a point on the graph of role="math" localid="1645806552504" y=f(x), which of the following points must be on the graph of y=f-(x)?

Determine whether each relation represents a function. For each function, state the domain and range.

-1,0,2,3,4,0

The inequality-1<x<3can be written in interval notation as___________.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free