## Denebel 3 years ago A particle moves along the x-axis so that its position at any time t> 0 is given by x(t) = t^4 - 10t^3 + 29t^2 - 36t +2. For which value of t is the speed the greatest?

1. experimentX

find maxima

2. Denebel

Maximum at first derivative or second?

3. experimentX

o.. sorry, take derivative ... the resulting function will give you speed.

4. experimentX

and the usual process of maxima

5. Denebel

|dw:1334044638555:dw| The derivative graph looks something like this... where is the maximum?

6. experimentX

do we have any interval of time given??

7. Denebel

No, t>0

8. experimentX

it seems that we have local maximum but's that negative ... I guess at infinity then.

9. Denebel

Lol, but it's multiple choice.. A. t= 1 B. t= 2 C. t= 3 D. t= 4 E. t=5

10. experimentX

the distance is actually decreasing.

11. experimentX
12. experimentX
13. Denebel

What does that mean for speed? Sorry, I do not understand..

14. experimentX
15. experimentX

speed is rate of change of distance ... should always be positive.

16. Denebel

Oh, ok thanks.