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Math Help - Having trouble with basic Derivatives

  1. #1
    Newbie Cdoddsy's Avatar
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    Question Having trouble with basic Derivatives

    Allright, I went to the lecture, read the section in my math book, and watched videos on youtube..., but still...how to arrive to the answer to this problem eludes me.

    Problem:

    Find an equation of the tangent line to the curve at the given point.

    y = (x-1)/(x-2), (3,2)

    Equation that the book gives to solve this problem:

    M = lim x -> a [f(x) - f(a)] / [x - a] where point (a, f(a))

    My Work:

    f(x) = (x-1)/(x-2)
    f(a) = 2
    a = 3

    ---

    M= [[(x-1)/(x-2)] - 2] / [x-3]

    ---

    M= [(x-1)/(x-2) - (2x-4)/(x-2)] / (x-3)

    ---

    M= [(-x+3)/(x-2)] / (x-3)

    ---

    M= (-x+3) / [(x-2)(x-3)]

    ~This is as far as I get. I have no idea if I am correct so far. All I know is that I am not getting the answer that the book gives in the back~

    Answer the book gives: y = -x+5

    Please help.
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  2. #2
    MHF Contributor
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    You need to remember to take the \lim_{x \to a} part down each time...

    Assuming you had done this you would have gotten to

    M= \lim_{x \to 3}\frac{(-x + 3)}{(x - 2)(x - 3)}

     = \lim_{x \to 3}\frac{-(x - 3)}{(x - 2)(x - 3)}

     = \lim_{x \to 3}\frac{-1}{x - 2}

     = \frac{-1}{3 - 2}

     = -1.


    So that means for your tangent line, which is of the form y = Mx + c, that M = -1.


    So you have y = -x + c.

    Use the point that lies on the curve to find the value of c.
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