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Numerade Educator

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Problem 39 Hard Difficulty

Find $ f $.

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

Answer

$-x^{2}+2 x^{3}-x^{4}+12 x+4$

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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.