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Math Help - Cubic Equation

  1. #1
    Member classicstrings's Avatar
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    Cubic Equation

    A curve with equation y = ax^3 + bx passes through the origin at an angle of 45 degrees and passes through the point (2,-6)

    FInd values a and b.

    Not sure how to tackle this question! Thanks.
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  2. #2
    Member Glaysher's Avatar
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    Ange of 45 degrees will mean a gradient of 1

    Differentiate to find dy/dx

    Know dy/dx = 1 when x = 0

    And from given point y = -6 when x = 2

    Creates two simultaneous equations which you can solve to find a and b
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  3. #3
    Eater of Worlds
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    They give you the slope, 45 degrees. That's a slope of 1

    Set up your derivative and set it equal to 1 at the origin:

    \frac{d}{dx}[ax^{3}+bx]=3ax^{2}+b

    3a(0)^{2}+b=1...[1]

    Your equation must pass through (2,-6)

    a(2)^{3}+b(2)=-6....[2]

    Solve [1] and [2] for a and b.
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  4. #4
    Member classicstrings's Avatar
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    Thanks a lot! Cheers!
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