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Math Help - Please help with derivatives and functions

  1. #1
    ZKR
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    Please help with derivatives and functions

    Hello,
    I`m a total noob in math and barely remember anything from high school past one variable equations.
    If someone can help me with several issues here, I`d be most appreciated.

    It is given that the second derivative of a function is g"(x) = 4
    and that g`(0) = 0 and g(0) = 4.
    What`s the function g(x) ?

    Any help is most appreciated.
    Thanks
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  2. #2
    fkf
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    Re: Please help with derivatives and functions

    We have
    g''(x) = 4, g'(0) = 0 and g(0) = 4

    Start with the function g''(x) = 4 and find its primitive function
    g''(x) = 4 => g'(x) = 4x+C

    Since g'(0) = 4 we have
    g'(x) = 4x+C => 4*0+C = 0 <=> C = 0

    Finding the primitive function of f'(x) gives us
    g'(x) = 4x => g(x) = 2x^2+D

    Since g(0) = 4 we have
    g(x) = 2x^2+D => 4 = 2*0^2+D <=> D = 4

    Thus, g(x) = 2x^2+4
    Last edited by fkf; November 5th 2012 at 08:04 AM.
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  3. #3
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    Re: Please help with derivatives and functions

    g''(x) = 4

    antiderivative ...

    g'(x) = 4x + C

    g'(0) = 0 \implies C = 0

    g'(x) = 4x

    antiderivative ...

    g(x) = 2x^2 + C

    g(0) = 4 \implies C = 4

    g(x) = 2x^2 + 4


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  4. #4
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    Re: Please help with derivatives and functions

    Quote Originally Posted by fkf View Post
    We have
    g''(x) = 4, g'(0) = 4 and g(0) = 4
    The problem gave g'(0)= 0.

    Start with the function g''(x) = 4 and find its primitive function
    g''(x) = 4 => g'(x) = 4x+C

    Since g'(0) = 4 we have
    g'(x) = 4x+C => 4*0+C = 4 <=> C = 4

    Finding the primitive function of f'(x) gives us
    g'(x) = 4x+4 => g(x) = 2x^2+4x+D

    Since g(0) = 4 we have
    g(x) = 2x^2+4x+D => 4 = 2*0^2+4*0+D <=> D = 4

    Thus, g(x) = 2x^2+4x+4
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  5. #5
    fkf
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    Re: Please help with derivatives and functions

    Oh, my bad. Sorry for that.
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  6. #6
    ZKR
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    Re: Please help with derivatives and functions

    Thanks guys.
    It was very helpful.

    Next time I`ll post in the appropriate forum.
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