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Math Help - Equation of tangent - Help!

  1. #1
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    Equation of tangent - Help!

    Hi, I have the problem:

    'Find the equation of the tangent to the curve with equation  y=x^3 - x^2 - 6x - 2 at the point where  x=1.'

    I'm sure you'd have to use synthetic division (polynomials) at some point but I am not sure.

    Many thanks.
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  2. #2
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    Quote Originally Posted by Stepheennnnn View Post
    Hi, I have the problem:

    'Find the equation of the tangent to the curve with equation  y=x^3 - x^2 - 6x - 2 at the point where  x=1.'

    I'm sure you'd have to use synthetic division (polynomials) at some point but I am not sure.

    Many thanks.
    Nope, you just have to differentiate the function.

    y' = 3x^2 - 2x - 6

    edit: I didn't see x=1 as a point.

    First get the y co-ordinate at the point where x=1

    y = 1^3-1^2-6-2 = -8 to give the ordered pair (1,-8)

    y'(1) = 3(1^2)-2-6 = -5

    The gradient, m, is therefore -5.

    Use the equation of a straight line and the ordered pair above to get the equation.

    y = -(5x+13)
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  3. #3
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    Aah, now I get it.
    Thank you!
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  4. #4
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    Just noticed there's a second part to the question which has just confused me. It says 'Find the coordinates of the point where this tangent meets the curve again.' Any ideas?

    Thanks.
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