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Problem

Find $ f $. $ f"(x) = x^6 - 4x^4 + x + 1 $
02:32

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Problem 25 Easy Difficulty

Find $ f $.

$ f"(x) = 20x^3 - 12x^2 + 6x $

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02:25

Fahad Paryani

Related Courses

Calculus 1 / AB

Calculus 2 / BC
Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Related Topics

Derivatives

Differentiation

Volume

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Top Calculus 2 / BC Educators
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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

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Problem 9
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Problem 16
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Problem 25
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Problem 28
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Problem 75
Problem 76
Problem 77
Problem 78
Problem 79

Video Transcript

So for this problem here we are given um F double prime of X. And we want to find F. So we have capital prime of X. Given to us by 20 X cubed the complete -12 x squared plus six X. We take the first anti derivative. So F prime of X. This is going to be equal to 20 X to the fourth over five. That's going to be four X. To the fourth minus 12 X. Cubed over three. So that's minus four X cubed plus six X squared over two. So it's gonna be three X squared. Then we find F. That's gonna give us four X. To the fifth over five. So we have 4/5 X to the 5th minus four X. To the fourth over four fascist X. To the fourth plus three X cubed over three. That's just going to be executed. Um And then we have to remember that here we had to add our plus C. So here it's gonna be plus C. X Plus D. So that would be how we show this whole thing. This is gonna be to the fourth over force. This would be five. Which makes this a one. This would be our final answer.

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Related Topics

Derivatives

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Video Thumbnail

04:35
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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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