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Math Help - Integral

  1. #1
    Member Awsom Guy's Avatar
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    Integral

    A curve has its gradient functions as (2ax-b). It passes through the origin and (2,8) is its maximum point. Find a, b, and the equation of the curve.

    I know a couple of things that its got something to do with the word maximum and make sure you understand and (2,8) as its maximum point.
    I have no working to give as I have no idea where to begin.
    Thanks
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  2. #2
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    Quote Originally Posted by Awsom Guy View Post
    A curve has its gradient functions as (2ax-b). It passes through the origin and (2,8) is its maximum point. Find a, b, and the equation of the curve.

    I know a couple of things that its got something to do with the word maximum and make sure you understand and (2,8) as its maximum point.
    I have no working to give as I have no idea where to begin.
    Thanks
    If f'(x) = 2ax - b and (2, 8) is the maximum, then f'(2) = 0.

    Therefore 2a(2) - b = 0

    b = 4a.



    f(x) = \int{2ax - b\,dx}

     = ax^2 - bx + c

    And since the curve passes through (0, 0) and (2, 8) substitute these values into f(x) and you will end up with some equations you can solve simultaneously for a, b, c.
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  3. #3
    Member Awsom Guy's Avatar
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    Sorry I dont get that and whats the big F looking thing sorry that stuff I haven;t learnt.
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    Quote Originally Posted by Awsom Guy View Post
    Sorry I dont get that and whats the big F looking thing sorry that stuff I haven;t learnt.
    I haven't used a big F...
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  5. #5
    Member Awsom Guy's Avatar
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    umm.. the big \int thing.
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    Quote Originally Posted by Awsom Guy View Post
    umm.. the big \int thing.
    It's the integral sign, and it stands for the indefinite integral, also known as the antiderivative.

    So I'm saying take the antiderivative of that function.
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  7. #7
    Member Awsom Guy's Avatar
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    ok thanks
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  8. #8
    Member Awsom Guy's Avatar
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    but where does the dx come from.
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    Quote Originally Posted by Awsom Guy View Post
    but where does the dx come from.
    It's just notation.

    It means take the antiderivative of the function with respect to the variable x.

    It's important for when you learn the reverse chain rule.
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  10. #10
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    so I get:
    C=0 and:
    8=4a^2-2b+C
    How can I simultanously solve this.
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    Quote Originally Posted by Awsom Guy View Post
    so I get:
    C=0 and:
    8=4a^2-2b+C
    How can I simultanously solve this.
    You know that c = 0 and b = 4a. Substitute them in.
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  12. #12
    Member Awsom Guy's Avatar
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    does a equal to: (8)/(4a-8)
    thanks
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  13. #13
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    these are meant to be the answers:
    a=-2
    b=-8
    y=-(2x^2)-8x
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    Quote Originally Posted by Awsom Guy View Post
    these are meant to be the answers:
    a=-2
    b=-8
    y=-(2x^2)-8x
    You should be getting a quadratic equation in a. You'd need to factorise or use the Quadratic formula to evaluate a.
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  15. #15
    Member Awsom Guy's Avatar
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    Sorry I am just not getting this, I'll just skip this question thanks anyways.
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