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Math Help - Use integral calculus to solve differential equation problems

  1. #1
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    Use integral calculus to solve differential equation problems

    Please help me to answer this, thank you!

    Find the equation of the curve that satisfies the differential equation f"(x) = 6x - 12 and which passes through the points (0, -8) and (1, -1).
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by LilDragonfly
    Please help me to answer this, thank you!

    Find the equation of the curve that satisfies the differential equation f"(x) = 6x - 12 and which passes through the points (0, -8) and (1, -1).
    f(x)=x^3-6x^2+ax+b
    Sooooo:

    f(0)=-8 = 0^3-6*0^2+a*0+b=b
    Thus b = -8.

    f(1)=-1=(1)^3-6(1)^2+a(1)-8
    gives:
    -1=1-6+a-8=-13-a
    or
    a = 12

    -Dan
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  3. #3
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    I do not know if you understood what topsquak said, but when you have,
    f''(x)=6x-12
    It means if you integrate both sides you have,
    f'(x)=3x^2-12x+a with some constant a,
    the reason to why f''(x) becomes f'(x) is because when you integrate a derivative of a function you get back the function (definition of integral). So when you have f''(x) integrating once would yield f'(x) so you need one more time:
    f(x)=x^3-6x^2+ax+b
    Then use topsqaurk post to complete the problem.
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