1. ## 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.

2. 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:

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

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

$\displaystyle x=t^3-t=0$.

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

$\displaystyle \frac{dx}{dy}=\frac{dx}{dt}\frac{dt}{dy}=0$

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

$\displaystyle \frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx}=0$.

RonL

3. The points where the tangent is parallel with the line $\displaystyle y = x$ to the solutions of:

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

4. Originally Posted by Glaysher
The points where the tangent is parallel with the line $\displaystyle y = x$ to the solutions of:

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