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Math Help - Find the slope of the tangent to the curve

  1. #1
    s3a
    s3a is offline
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    Find the slope of the tangent to the curve

    Find the slope of the tangent to the curve

    y = 3 + 4x^2 - 2x^3

    at the point where x = a.

    Answer: 8a - 6a^2

    I have no idea how to answer this question since it doesn't give me any points to work with.

    Any help would be greatly appreciated!
    Thanks in advance!
    Last edited by s3a; September 26th 2009 at 08:50 PM.
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  2. #2
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    Differentiate it

     y = 3 + 4x^2 - 2x^3

     y' = 8x - 6x^2

    y' is also known as the gradient function. so when x = a, the gradient would be equal to? substitute x = a for all x values

     y' = 8(a) - 6(a)^2

     = 8a - 6a^2

    therefore, the slope of the tangent is equal to  = 8a - 6a^2
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