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Math Help - Vector functions

  1. #1
    Braas
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    Vector functions

    Hi I have some vector function problems I'd like some help for, but I didn't see a forum for them so I'll start by posting one problem in case people don't know them.

    I don't know all the english math terms so pardon me if the problem may seem like nonsense

    I have a vector function, f(t)= (t^3-t, 3t+1).

    I need to find all the cross points with the y-axis
    All the points where the tangent is vertical
    and all the tangents that are parallel with the line y=x

    Thanks in advance and feel free to correct my math terms, be they wrong.

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Braas
    Hi I have some vector function problems I'd like some help for, but I didn't see a forum for them so I'll start by posting one problem in case people don't know them.

    I don't know all the english math terms so pardon me if the problem may seem like nonsense

    I have a vector function, f(t)= (t^3-t, 3t+1).

    I need to find all the cross points with the y-axis
    All the points where the tangent is vertical
    and all the tangents that are parallel with the line y=x

    Thanks in advance and feel free to correct my math terms, be they wrong.

    Write:

    x=t^3-t and y=2t+1.

    1. Then the points where this crosses the y axis correspond to the roots of

    x=t^3-t=0.

    2. The points where the tangent is vertical correspond to the solutions of:

    <br />
\frac{dx}{dy}=\frac{dx}{dt}\frac{dt}{dy}=0<br />

    3. The points where the tangent is horizontal corespond to the solutions of:

    <br />
\frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx}=0<br />
.

    RonL
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  3. #3
    Member Glaysher's Avatar
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    The points where the tangent is parallel with the line y = x to the solutions of:

    \frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx} = 1
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Glaysher
    The points where the tangent is parallel with the line y = x to the solutions of:

    \frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx} = 1
    Opps, I had miss-read that part of the question!

    (it might be more convienient in this case though to look at solutions of:

    \frac{dx}{dy}=\frac{dx}{dt}\frac{dt}{dy} = 1

    instead, as dx/dt and dt/dy are easier to compute than dy/dt and dt/dx)

    RonL
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