/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 87 Prove that every nonconstant lin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 87 (page 263)

Prove that every nonconstant linear function is either always increasing or always decreasing.

Short Answer

Expert verified

It is proved that every nonconstant linear function is either always increasing or always decreasing.

Step by step solution

01

Step 1. Given Information

We are given that every nonconstant linear function is either always increasing or always decreasing.

02

Step 2. Proving the statement

Consider a function of the form,

f(x)=mx+b;wherem鈮�0.

That is f is a non-constant linear function.

The first derivative of the function is,

f'(x)=ddx(mx+b)=m路1+0=m

Therefore, f is either positive or negative.

If m is positive, the function is increasing. If m is negative then the function is decreasing. So, every non constant linear function is either always increasing or always decreasing.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Restate Rolle鈥檚 Theorem so that its conclusion has to do with tangent lines.

Find the possibility graph of its derivative f'.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=3x-2x

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=lnx2+1
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.