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Math Help - Finding f

  1. #1
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    Finding f

    I need help getting the antiderivative.

    Find f.

    f '(x)= (3x + sqrt(x) + 4)/(x^2); f(1)= -1

    I got: f '(x)= 3/x + 1/x^(3/2) + 4/x^2

    I broke it up so each piece is under x^2.

    Is this wrong?
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  2. #2
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    Re: Finding f

    Just need to integrate each by the addition and power rules; then plug in the f(1)=-1.
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  3. #3
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    Re: Finding f

    Getting the antiderivative from my reduced equation is what I need help getting
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  4. #4
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    Re: Finding f

    What you have done is in the right direction, I would write:

    f'(x)=3x^{-1}+x^{-\frac{3}{2}}+4x^{-2}

    Now use the power rule for integration term by term, then use the given point (1,-1) to determine the constant of integration, or use the boundaries as limits for definite integrals. The first method is probably more familiar.
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  5. #5
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    Re: Finding f

    For the integral I got F(x)= 3lnx - 1/(1/2sqrt(x)) - 4/x

    I keep getting this. I dont believe for it to be right?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Finding f

    Yes, that's right (but don't forget the constant of integration), I would write this as:

    f(x)=3\ln(x)-\frac{2}{\sqrt{x}}-\frac{4}{x}+C

    Now, use f(1)=-1 to find C.
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  7. #7
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    Re: Finding f

    Okay. I got C = 5. So now I believe the equation is:
    F(x)= 3lnx - 2/sqrt(x) - (4/x) + 5

    Is this the correct format to write in?
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Finding f

    Yes, that's correct, although you don't need the parentheses around 4/x, but they don't make it incorrect.
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  9. #9
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    Re: Finding f

    I just did that so you can see its together. Thank you!
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