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Math Help - Finding equation of a Tangent Line

  1. #1
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    Finding equation of a Tangent Line

    Find an equation of the line that is tangent to the graph of f and parallel to the given line.

    Function: f(x) = 2x^2

    Line: 4x y + 4 = 0

    Tell me what I'm doing wrong. According to my instructor's directions:

    Step 1. Find the slope of the tangent line:



    Do the algebra, reduces to 4x-2h - the limit/slope is 4x.

    Step 2. Find the slope of the given line:


    4x y + 4 = 0 same as y=4x+4 and so m=4

    Step 3. Set the slope of the tangent equal to the slope of the given line, and solve for x.

    4x=4 so x=1

    Step 4. Use the values from above to find the equation of the line.

    (So elsewhere in the lecture, he mentions that if x=1, then your reference point is (1,1) - if someone else can explain why, I'd appreciate that too. I'm not getting that. But assuming that it is....)

    y-1=4(x-1)

    y-1=4x-4

    y=4x-3


    Why isn't this right? What am I missing? I'm sure it's something obvious and dumb?
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  2. #2
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    y - f(1) = 4(x - 1)

    f(x) = 2x^2

    f(1) = 2<br />

    y - 2 = 4(x-1)

    y = 4x - 2
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  3. #3
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    Nevermind. Naturally that "thing he said that made no sense to me" was the source of the problem, and I had to plug x back into the function to get y. Duh.

    But thank you Skeeter!
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