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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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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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