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) = 2x^2 - 3x + 1 $, $ [0, 2] $

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

Hosmay L.

March 29, 2022

what is the point of plugging what we found from the f(a) and f(b) into the equation that we have from the theorem?

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

04:26

Verify that the function s…

01:25

0:00

04:15

01:10

Determine whether the give…

Okay, so now we're being asked to verify that the function f satisfies two hypothesis of the mean Barry doing on the Cuban interval. And then we're supposed to find all the numbers sees that satisfies the conclusion of the mean value they're here. We call that affects because to explore monastery experts one on the closing of war from zero to. So since dysfunction is a paranormal, we know automatically that it is continuous on the clothes. Wonderful was there too. And it was also defendable on Jura Institution That is a property of a polynomial function. So So now that this satisfies two two conditions required for Rose there, I mean for the mean value there. I apologize. We can test the conclusion. But I mean right there. And she'll just recall the conclusion for the main fire demons that there exists a number see, such that is the derivative of prime of C. There is a value where the average slope from A to B equals that there's a sea that give this a tangent line that had the same slope. So now that this satisfies this conditions, R B is too in our eight zero so the first thing I'm going to do is figure out what effort to is. And if you plug in your number into the function, do you get three? What? And half of one ISS. I mean, I'm I'm sorry. Half of zero is just equal to warn. So now I'm going to plug in all these numbers into my mean various room. The prime of C. We're going to come back to this ever be is in this case, three minus F zero, which is one what over two minus zero was then gives it to over too, which is simply one. And now all we have to do is now take the derivative of this function in terms of seeing. So now it's going to be Ah, so just do it like you regularly do. So did you ever have of axis for sea? Minus three is equal to one. So now we're looking for a sea that satisfies this condition. And now well, move over here. We're going to add the three to this side. Three, two, both side, and then we're going to get foresee is equal to for was Jen, give this see of one that is the number at us. They see a satisfying conclusion of the mean guy item, and in this case there's only one seat. So that is the correct answer.

View More Answers From This Book

Find Another Textbook

00:44

At most, Keith can spend $90 on sandwiches and chips for a company lunch. He…

01:08

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. …

01:49

3. Fill in the blanks with center, circle, directrix, focus, line, parabola,…

01:26

he data set gives the number of hours it took each of the 10 students in a c…

IF 24% of the sixth grade class is in Mrs Whites class and Mrs White has 30 …

01:28

Mr rowley has 16 homework papers and 14 exit tickets to return. Ms ribera ha…

1. What is the most important rule to remember when solving inequalities wit…

A container has 3 apple juice boxes, 4 grape juice boxes and 5 orange juice …

01:11

4 people can dig a hole 20m deep in 3 hours. How long will 25 people take to…

02:25

What equation represents a population of 490 animals that increases at an an…