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Math Help - find a vector

  1. #1
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    find a vector

    how to find the vector that tangent to the parabola y=x^2 at (2,4) ??
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  2. #2
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    Quote Originally Posted by theliong View Post
    how to find the vector that tangent to the parabola y=x^2 at (2,4) ??
    It will be a 2D vector, and parallel to the line defined by the tangent at that point.

    To find the tangent, which will be of the form y = mx + c, to find m, take the derivative, then evaluate the derivative at that point.

    y = x^2

    \frac{dy}{dx} = 2x

    \frac{dy}{dx}|_{x = 2} = 4.


    Thus m = 4.


    We have

    y = 4x + c

    We also have (x, y) = (2, 4) as a point on the tangent.

    So 4 = 4\cdot 2 + c

    c = -4.


    Thus the tangent is y = 4x - 4.


    So you will have a vector that is parallel to y = 4x - 4 and that passes through (x, y) = (2, 4).

    Can you go from here?
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  3. #3
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    The answer is <1,4>. How to evaluate from y=4x-4 until <1,4>??

    Quote Originally Posted by Prove It View Post
    It will be a 2D vector, and parallel to the line defined by the tangent at that point.

    To find the tangent, which will be of the form y = mx + c, to find m, take the derivative, then evaluate the derivative at that point.

    y = x^2

    \frac{dy}{dx} = 2x

    \frac{dy}{dx}|_{x = 2} = 4.


    Thus m = 4.


    We have

    y = 4x + c

    We also have (x, y) = (2, 4) as a point on the tangent.

    So 4 = 4\cdot 2 + c

    c = -4.


    Thus the tangent is y = 4x - 4.


    So you will have a vector that is parallel to y = 4x - 4 and that passes through (x, y) = (2, 4).

    Can you go from here?
    Follow Math Help Forum on Facebook and Google+

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