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Find $ f $. $ f"(x) = 8x^3 + 5 $, $ \quad f(1)…

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Problem 39 Hard Difficulty

Find $ f $.

$ f"(x) = -2 + 12x - 12x^2 $, $ \quad f(0) = 4 $, $ \quad f'(0) = 12 $

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Amrita Bhasin

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Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

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Differentiation

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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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Video Transcript

For this problem, what we have is F double prime of X. Yeah. Is equal to negative two plus 12 X -12 x squared. So when we find a crime affect you see that this is going to be equal to a negative two acts Plus six x squared minus for x cube class C. But we know that F prime of zero is 12. That means that F prime of zero C is going to be 12. Then we take the uh 100 that that's the U. S. And negative X squared plus to act cube minus X to the fourth plus 12 X plus some other constant. But we know that F of zero is four. So based on that, we know that this is plus four final answer.

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Calculus: Early Transcendentals

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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

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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