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Find $ f $.

$ f"(x) = 4 + 6x + 24x^2 $, $ \quad f(0) = 3 $, $ \quad f(1) = 10 $

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01:53

Wen Zheng

00:50

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Oregon State University

Harvey Mudd College

Baylor University

Lectures

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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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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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Find $f(x)$ if $f^{\prime}…

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Find $f(3)$ and $f(-1)$.

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Find $f$ such that:$$f…

So picking we have the second derivative of X. And it's equal to four plus six X plus 24 X. Screwed. So when we evaluate this, when you take F prime of X using the anti derivative we get four X plus um free X squared plus. He acts cute Classy. But we know that F of zero is three. So what we're gonna end up getting is Or f of f prime of one is 10. So we're going to end up getting to as R. C value. Then we have F of X. Which is going to give us um to have squared plus X cubed Class two X to the 4th plus two X plus another constant value. But we know that F of zero is three. That means as constant as three. Therefore our final anti derivative is two X squared plus X cubed plus two X. To the fourth plus two X plus three. Final answer.

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