Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers $ c $ that satisfy the conclusion of the Mean value Theorem.

$ f(x) = 1/x $, $ [1, 3] $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Fahad Paryani

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 2

The Mean Value Theorem

Derivatives

Differentiation

Volume

Harvey Mudd College

Baylor University

University of Nottingham

Idaho State University

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

0:00

Verify that the function s…

01:25

04:26

03:21

Verify that the hypotheses…

01:58

Okay, so now we're being asked to verify that the function stratified to me about their monthly given interval. And then we're are being told to find all number sees that satisfy the conclusion of the mean value. So in order to know whether this function is continuous on wonder three, I think the best way to approach just one is to craft affects equals one of Rex. And so the graph of one over X looks something like this. It certainly does not defined it. Zero in Ashley goes off too positive infinity from the right and then to negative infinity from the left like that looks something like that and centre and of those only from like from one two, three was just probably approximately along this line right here. We know that just by looking at it, we know it's continuous, so it is definitely continue. And you can see that is also defensible because we can take attention at any point along this line, a wrong d's along this interval. So this is also differential. So now that we have satisfies the conditions for the mean value, then we can apply the virus. You can apply and find the conclusions of the medieval Gotham. And so the conclusion states that there is a number see such that and the derivative of every Becks that Point C will give us the same slope as the average float between between in the interval from wonder to be, which just means that effort to me. Minus half of one over three minus one. That is how you find the ever slope from one the one and with those apply this right away. So the value of efforts to be so we simply plug in effort three into original function in that gives us go on third and you can plug in one and that gives us one. And we can now apply this to our average slope, which will then give us. Ah, wondered. Minus one over two. And a derivative of one over X can be rewritten. So this remember that this function one of Rex can be re written as accident negative one, and you can take your do it if I bring this down. And then it's a plaque on this by one which will then give us. We're going to write this in terms of C So this gives us a negative one oversea squared. And now we're simply going to subtract one. So get negative one of the C squared equal to negative two thirds all over, too. I'm gonna bring this to the next page, and that is our negative two thirds over to just simply give us one third. So that is equal to negative one third. And now we just flip this and the negatives canceled. This just gives a C squared seacoast three and we take the square root of both side. And remember, squared gives us a plaster mining. This is plus or minus three three. And our interval, as you recall, is only from one to three sets all positive numbers. So the negative Route three actually is not included in our answer. So this is only part of the three. That is our answer.

View More Answers From This Book

Find Another Textbook

01:43

central angle of 3 radians cuts off an arc of length 18 inches_ Find the are…

04:04

A clinical trial was conducted to test the effectiveness of dnug for treatin…

04:59

3) Find the limit: Do not use L'Hopital' s rule:x2 + 2x-8 lim …

04:11

2. A certain farm produces homemade potato chips that is sells in bags "…

01:45

Use the Factor Theorem to determine whether the linear polynomial is factor …

01:40

Find all trigonometric functions of angle 8 if: Sin 8 = J andcos 8 <0…

02:38

Diego claims that he can tell; using slopes, that this quadrilateral is a pa…

02:22

There are 10 marbles in a bag (4 solid, 6 striped)What is the likelihood…

03:28

point)It can be shown that Y1 x" Y2 =x 6 and Y3 = 7 are solutions t…

01:03

Tuetap9or9 T2 Is the graph of y = |xl translaled how many unlts and In w…