Problem

Verify that the function satisfies the three hypo…

05:09

Question

Answered step-by-step

Problem 5 Easy Difficulty

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers $ c $ that satisfy the conclusion of Rolle's Theorem.

$ f(x) = 2x^2 -4x + 5 $, $ [-1, 3] $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Fahad Paryani

Numerade Educator

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

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 2

The Mean Value Theorem

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Video Transcript

Okay, So this questions asking us to verify the front that the function after practical to x square manage for class five satisfies two three hypothesis of roll student on the given interval Andan We have to find the number of sees that satisfies the conclusions of roast him. So here we know that after Max tickles too X square minus four plus five. So just by looking at this function, we know it is a poly normal because it has a a function of degree greater than one So here too So we know this is appalling amore and all polynomial czar continuous and they're also all defensible. That is sick That is the property of all polynomial. So we know off the back that thiss thes two conditions continuous and defense ability are are given of upon your meal And if you actually plug in the values of negative ones So if you plug in aa two of negative one squared minus four times negative one plus five, you get yesterday get eleven And if you do the same thing for three so now you plug in three the two times to re squared minus four times three plus five. It also gives you eleven. So we know that half of negative one and efforts three are also satisfied is also a truth statement. So now that we satisfied all the three conditions required for a roasted um, we can go ahead and find the numbers of sees that satisfies the astral conclusion. And so the recall the conclusion of this serum is that they that we know that there will be a number see, in the interval Judge that the director of the derivative at point C is equal to zero. So we have a horizontal line and we'll get you salt for this in this case. So if we take the duty of effort back so the derivative of F Prime I mean F Prime Vex, which is just a derivative. We can find that the derivative of effort back is just for eggs minus for and all they're doing is looking for where this function in the Cordillera. So all we do is set this function equal to zero. Then we just bring the fourth to the other side. So we get four x equal four on DH X equals one in self Rex and This is also our number, See, because if you plug in this value one, the four times one is one I'm in for ten points. Four minus four zero. So that is the sea that satisfied the conclusion? Of course, dear. Hey, there's our answer.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem