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Numerade Educator

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Problem 43 Medium Difficulty

Find $ f $.

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

Answer

$$
f(x)=2 x^{2}+x^{3}+2 x^{4}+2 x+3
$$

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Video Transcript

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.