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anonymous

  • 4 years ago

Let f(t)=4 t^2 + 4/t^2. Find the slope of the curve at t = -3.

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  1. radar
    • 4 years ago
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    f(t)'=8t -(8)/t^3 for t=-3 -24-8/27 -640/27=-20

  2. radar
    • 4 years ago
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    Ooop it is not -20 -640/27=-23.7037

  3. anonymous
    • 4 years ago
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    yeah I got df/dt=8t-2/t^2 so t=-3 => 8*(-3)-2/(-3)^2 -24-2/9 ! but i dont trust my work

  4. radar
    • 4 years ago
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    the second term when you differentiated;\[4 \over t ^{2}\]is\[4 t ^{-2}\]becomes \[-8 t ^{-3}\]

  5. radar
    • 4 years ago
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    or\[-8\over t ^{3}\]

  6. anonymous
    • 4 years ago
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    but I would still have to plug in -3 for t

  7. radar
    • 4 years ago
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    Yes indeed.

  8. anonymous
    • 4 years ago
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    wait was I on the right track to getting the answer?

  9. radar
    • 4 years ago
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    that would be -8/27 for that term and 24 for the first term I see what you mean it can't be negative with 24 being positive!! lol, I better take a nap.

  10. anonymous
    • 4 years ago
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    but -640/27=-23.7037 is the answer

  11. anonymous
    • 4 years ago
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    right?

  12. radar
    • 4 years ago
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    Oh yes, thats right as t=-3 so it would be -24 and a negative 8/27 that means we have to combine the -24 and the -8/27 giving -648/27 - 8/27=-656/27= -24.29

  13. radar
    • 4 years ago
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    Looking at your next to last post. How did you get -640/27? Wouldn't -24 X 27 =-648 ??

  14. radar
    • 4 years ago
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    It would appear so, if I have kept track of the signs.

  15. radar
    • 4 years ago
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    But maybe I messed up let me think about this?

  16. anonymous
    • 4 years ago
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    lol take your time

  17. radar
    • 4 years ago
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    I think I did mess up on that 2nd term when I plugged in the minus 3\[-8\over t ^{3}\]\[-8\over (-3)^{3}\]\[-8\over -27\] or POSITIVE 8/27 lol there it is.

  18. radar
    • 4 years ago
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    So we ADD the 8/27 to the negative 648/27 giving -640/27 So sorry paunic88, I did stray off the path of keeping track of signs.

  19. anonymous
    • 4 years ago
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    ok so the final anwser is -640/27 right? (ill compute it later)

  20. radar
    • 4 years ago
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    -3 X -3 X -3 = -27 lol

  21. radar
    • 4 years ago
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    Yes.

  22. radar
    • 4 years ago
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    Good luck with your studies,and don't err with signs lol

  23. anonymous
    • 4 years ago
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    ok thank you very much for the help

  24. radar
    • 4 years ago
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    ur welcome.

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