Chapter 3: Q. 3 (page 259)

State the definition of what it means for a function $f$ to be increasing on an interval $I$ and what it means for a function $f$ to be decreasing on an interval $I$ .

Short Answer

Expert verified

If for all $a$ and $b$ in the interval $I$ with $b > a$ , $f (b) > f (a)$ then the function $f$ is increasing in the interval $I$ .

If for all $a$ and $b$ in the interval $I$ with $b > a$ , $f (b) < f (a)$ then the function $f$ is decreasing in the interval $I$ .

Step by step solution

Step 1. Given Information.

Given the function $f$ defined in the interval $I$ .

Step 2. Increasing or Decreasing Function.

Determine where the function $f$ is increasing.

If for all $a$ and $b$ in the interval $I$ with $b > a$ , $f (b) > f (a)$ then the function $f$ is increasing in the interval $I$ .

Determine where the function $f$ is decreasing.

If for all $a$ and $b$ in the interval $I$ with $b > a$ , $f (b) < f (a)$ then the function $f$ is decreasing in the interval $I$ .

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!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

State the definition of what it means for a function $f$ to be increasing on an interval $I$ and what it means for a function $f$ to be decreasing on an interval $I$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Increasing or Decreasing Function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Calculus

Logic and Functions

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

State the definition of what it means for a function fto be increasing on an interval Iand what it means for a function fto be decreasing on an interval I.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Increasing or Decreasing Function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Calculus

Logic and Functions

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

State the definition of what it means for a function $f$ to be increasing on an interval $I$ and what it means for a function $f$ to be decreasing on an interval $I$ .