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I am trying to find $f(x)$ if I know that $$f''(x) = -2+12x-12x^2, \quad \; f(0)=4,\ f'(0)=12 $$

First I found the first derivative $$ f'(x)= -2x+6x^2-4x^3+C$$

and then I found the function, which is: $$f(x)=-x^2+2x^3-x^4+Cx+D$$

Now I am lost as to what to do with those values they gave me $ f(0)=4,\ f'(0)=12 $

Where do i proceed from here?

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    Plug in 0. And I assume the first $-2x$ is supposed to be $-2$?2012-07-11
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    Nope it should be $-2x$ since im finding the antiderivative right?2012-07-11
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    So i should plug in 0 for the second and 0 for the first and get those answers back?2012-07-11
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    first, in the $f'$ equation, plug in the point $(0,12)$ and solve for the constant $C$. Then do the same for $D$ in the $f(x)$ equation and you're done!2012-07-11

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