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Use the Intermediate Value Theorem to show that t…

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Problem 53 Medium Difficulty

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

$ x^4 + x - 3 = 0 $, $ (1, 2) $


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Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 5

Continuity

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
Grace He
Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Watch More Solved Questions in Chapter 2

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
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
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Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
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Problem 73

Video Transcript

All right. Um question asks you to use the intermediate value serum to show that there is a route Um of that polynomial in the interval from 1 to 2. Um Okay, so let's just look uh this is defined at the end points even though it's not included in the interval. So let's just look at what the value is. Well, even call it um Let's just call it F of x equals X. The four minus X plus x minus three. Let's make sure we coffee things down right? Um F of one since it is to find that one is one plus one minus three is negative one. And then f of two. Yeah. Is 2 to 4. 16 plus two minus three is positive 15. Okay, so let's just look on a graph where that is, so one comma negative one is there? And to calm a very big positive 15 is there? And uh this function is a polynomial. So it's continuous everywhere. In particular its continuous on that interval. So we've got to get from negative 12 positive 15. As we walk from 1 to 2. And there is no way that we can do that continuously without passing through zero. So the intermediate value theorem says uh there exists an X in the interval such that F of x equals zero. In fact we can we can choose any value between negative one and 15 and there would have to be a value where F of X equals that number. Um but for sure it works for zero

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Related Topics

Limits

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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