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Of the infinitely many lines that are tangent to …

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Problem 37 Hard Difficulty

Use Newton's method to find the coordinates of the inflection point of the curve $ y = x^2 \sin x $, $ 0 \leqslant x \leqslant \pi $, correct to six decimal places.


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Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Related Topics

Derivatives

Differentiation

Volume

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Lectures

Video Thumbnail

04:35

Volume - Intro

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.

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06:14

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Watch More Solved Questions in Chapter 4

Problem 1
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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

Video Transcript

question 37. We are looking at a function of why in court ex clear sign. So I took my group. Why? Ride and I had to use the, um Brad, It rule crying G plus g prime f So I have X sine X plus x where co sign IX and then I'm gonna take my Why Devil Crying and again I have to apply the chain of the product rule for both of these. No, I have to sign X plus two x coz I necks And then I'm looking at the second part plus two x coz my next And then when I take the g prime get a negative sign So it x weird sign Thanks. Combining my light terms I am going to get combine these two I have to sign of X plus we're ex sign Thanks My ex weird sign of necks And now I want my people why people cried So I take the derivative of to sign next which is just to sign Thanks. Then I have to do my product rule or four ex co scientific. So I get four co sign X minus were X sign of minus No on the last piece that minus two x sign of X minus X weird. Who? Sign X Combining my like terms. I am going to get six co sign of X minus six x sign of X minus X square Code signing Vicks. So I'm using, um, 1.5 is my approximate starting point. So I am putting in, um X minus a devil prime over F triple prime. And in your graphing calculator, if you put these in like l won our story, Why, 1123 white, four. And then you can just go to bars. And in white five, you can just have the wife. Why Double Brian? 1/4 bye bye. Why Triple crime? It's a lot easier on that. Right Did. So I got, um when I plugged in 1.5 into this right here, one x one, of course, people. Approximately 1.5. My first inflection point. And then I got accepted to 1.520092 ex of three. One point 519 855 And I also got that for, except for. So that becomes my ex value. And I put my ex value into my original wife function. And when I do that, when I do, uh, 1.519855 I get my value. 2.3 06 90 Yes, it's 90 six, Yeah.

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Related Topics

Derivatives

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Volume

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Kayleah Tsai

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Caleb Elmore

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Kristen Karbon

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Lectures

Video Thumbnail

04:35

Volume - Intro

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.

Video Thumbnail

06:14

Review

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.

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