/*! 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}

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 7 (page 313)

If f'(x)=g'(x)for all x鈭�[a,b], then for some constant C, f(x)=___ for all x鈭�[a,b].

Short Answer

Expert verified

If f'(x)=g'(x)for all x鈭�[a,b], then for some constant C, role="math" localid="1648539206646" f(x)=g(x)+C for all x鈭�[a,b].

Step by step solution

01

Step 1. Given information

The given statement is,

If f'(x)=g'(x)for all x鈭�[a,b], then for some constant C, f(x)=____for all x鈭�[a,b].

02

Step 2. Fill in the blanks

The given statement is a theorem

That is,

If f'(x)=g'(x)for all x鈭�[a,b], then for some constant C, localid="1648539633279" f(x)=g(x)+Cfor allx鈭�[a,b].

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

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

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

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=cos2(x)

It took Alina half an hour to drive to the grocery store that is 20 miles from her house.

(a) Use the Mean Value Theorem to show that, at some point during her trip, Alina must have been traveling exactly 40 miles per hour.

(b) Why does what you have shown in part (a) make sense in real-world terms?

Determine whether or not each function f in Exercises 53鈥�60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=x2鈭�1x2鈭�4,[a,b]=[鈭�3,3]
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.