1. ## Vector Functions

I started working on this problem but dont really know where to go.

The position function of a particle is given by .
At what time is the speed minimum?

I took the derivative of r(t) and got r'(t)=<-2t,-5,2t-4>. Where should i go from here? I dont really know what to do to solve for minimum t. Thanks for any help.

2. Originally Posted by palmaas
I started working on this problem but dont really know where to go.

The position function of a particle is given by .
At what time is the speed minimum?

I took the derivative of r(t) and got r'(t)=<-2t,-5,2t-4>. Where should i go from here? I dont really know what to do to solve for minimum t. Thanks for any help.
Speed is $s(t)=\left\| {r'(t)} \right\|$ which an be made minimum.

3. How do I figure out which t is minimum? Is is something like the first derivative test for regular functions?

4. Originally Posted by palmaas
How do I figure out which t is minimum? Is is something like the first derivative test for regular functions?
That is exactly the way to go.

P.S. This can really help you: $s(t) = \left\| {r'(t)} \right\| \Rightarrow \quad s'(t) = \frac{{r'(t) \cdot r''(t)}}{{\left\| {r'(t)} \right\|}}$

5. Thanks! I use that and find a min at t=2/3. I tried that as an answer, but it does not show as correct. Did I end up doing something wrong? I got s'(t)= (12t-8)/sqrt(8t^2-16t+41)