anonymous
  • anonymous
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?
Mathematics
chestercat
  • chestercat
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experimentX
  • experimentX
find maxima
anonymous
  • anonymous
Maximum at first derivative or second?
experimentX
  • experimentX
o.. sorry, take derivative ... the resulting function will give you speed.

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experimentX
  • experimentX
and the usual process of maxima
anonymous
  • anonymous
|dw:1334044638555:dw| The derivative graph looks something like this... where is the maximum?
experimentX
  • experimentX
do we have any interval of time given??
anonymous
  • anonymous
No, t>0
experimentX
  • experimentX
it seems that we have local maximum but's that negative ... I guess at infinity then.
anonymous
  • anonymous
Lol, but it's multiple choice.. A. t= 1 B. t= 2 C. t= 3 D. t= 4 E. t=5
experimentX
  • experimentX
the distance is actually decreasing.
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=x%28t%29+%3D+t%5E4+-+10t%5E3+%2B+29t%5E2+-+36t+%2B2
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=maxima+f%28t%29+%3D+4t%5E3+-+30t%5E2+%2B+58t+-+36
anonymous
  • anonymous
What does that mean for speed? Sorry, I do not understand..
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=maxima+d%28t%5E4+-+10t%5E3+%2B+29t%5E2+-+36t+%2B2%29%2Fdt
experimentX
  • experimentX
speed is rate of change of distance ... should always be positive.
anonymous
  • anonymous
Oh, ok thanks.

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