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Denebel

  • 4 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?

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  1. experimentX
    • 4 years ago
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    find maxima

  2. Denebel
    • 4 years ago
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    Maximum at first derivative or second?

  3. experimentX
    • 4 years ago
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    o.. sorry, take derivative ... the resulting function will give you speed.

  4. experimentX
    • 4 years ago
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    and the usual process of maxima

  5. Denebel
    • 4 years ago
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    |dw:1334044638555:dw| The derivative graph looks something like this... where is the maximum?

  6. experimentX
    • 4 years ago
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    do we have any interval of time given??

  7. Denebel
    • 4 years ago
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    No, t>0

  8. experimentX
    • 4 years ago
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    it seems that we have local maximum but's that negative ... I guess at infinity then.

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

  10. experimentX
    • 4 years ago
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    the distance is actually decreasing.

  11. experimentX
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=x%28t%29+%3D+t%5E4+-+10t%5E3+%2B+29t%5E2+-+36t+%2B2

  12. experimentX
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=maxima+f%28t%29+%3D+4t%5E3+-+30t%5E2+%2B+58t+-+36

  13. Denebel
    • 4 years ago
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    What does that mean for speed? Sorry, I do not understand..

  14. experimentX
    • 4 years ago
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    speed is rate of change of distance ... should always be positive.

  15. Denebel
    • 4 years ago
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    Oh, ok thanks.

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