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Math Help - Tangent line problem

  1. #1
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    Tangent line problem

    The two tangents that can be drawn from the point (3,5) to the parabola y=x^2 have slopes?

    -my steps
    y'=2x
    I know this is sad. But i just don't know what the question is asking i usually have all the tangent line questions down but this one is stumping me.


    The line y=3x+k is tangent to the curve y=x^3 when k is equal to?
    -my steps
    y'=2x
    2x=3x+k
    this doesn't make any sense and i think i am doing it wrong.



    All help is appreciated. Thanks
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by dandaman View Post
    The two tangents that can be drawn from the point (3,5) to the parabola y=x^2 have slopes?

    -my steps
    y'=2x
    I know this is sad. But i just don't know what the question is asking i usually have all the tangent line questions down but this one is stumping me.


    The line y=3x+k is tangent to the curve y=x^3 when k is equal to?
    -my steps
    y'=2x
    2x=3x+k
    this doesn't make any sense and i think i am doing it wrong.



    All help is appreciated. Thanks
    You were right by taking the derivative. The equation you got was:

    m = y' = 2x

    So for the point (3,5) you can use the equation we found from the derivative to calculate the slope at that point.

    (y-5) = m(x-3) *substitute your slope from the derivative in for m

    (y-5)= (2x)(x - 3)

    y = 2x^2-6x+5

    Then substitute this equation back into your original equation for y.

    2x^2 - 6x + 5 = x^2

    Get everything on one side and then find your x values either by factoring or quadratic formula.

    This will give you two x values on the two tangent lines. You can simply plug each of these into your slope equation m = 2x and that will give your their slopes.

    Using this info, see if you can work out the second one. Hope that helps!
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  3. #3
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    for the first one i got 1 and 5. Is this right?

    As for the second one,

    m=y'=3x^2
    so x must be at 1 since 3x^2=3x at x=1
    then k=0
    Is this right?

    Thanks for the reply man.
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  4. #4
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by dandaman View Post
    for the first one i got 1 and 5. Is this right?

    As for the second one,

    m=y'=3x^2
    so x must be at 1 since 3x^2=3x at x=1
    then k=0
    Is this right?

    Thanks for the reply man.

    Almost, you got your points right, but you need the slopes of those lines.

    Plug x=5 & x=1 into the x in your derivative m = y' = 2(x), THEN you will have your two slopes.

    You are correct for the second one! Good job!
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  5. #5
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    ok thanks a ton... You rock
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