Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q. 50 (page 249)

For each graph of f in Exercises 49–52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

Short Answer

Expert verified

The graph satisfies the mean value theorem and c=0

Step by step solution

01

Step 1. Given information

02

Step 2. Explanation

From the graph,

f(-1)=1f(3)=8

From MVT,

f'(c)=f(b)-f(a)b-a

f'(c)=f(-1)-f(3)-1-3

f'(c)=8-1-1-3

f'(c)=-74

c=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

For each set of sign charts in Exercises 53–62, sketch a possible

graph of f.

Determine whether or not each function f in Exercises 53–60 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 ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=x2−1x2−4,[a,b]=[−3,3]

Restate Theorem 3.3 so that its conclusion has to do with

tangent lines.

Sketch the graph of a function f with the following properties:

f is continuous and defined on R;

f has critical points at x = −3, 0, and 5;

f has inflection points at x = −3, −1, and 2.

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=2x-15
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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