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zeesbrat3

  • one year ago

A particle moves along the x-axis with position function s(t) = xe^x. How many times in the interval [−5, 5] is the velocity equal to 0?

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  1. zeesbrat3
    • one year ago
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    @saseal

  2. IrishBoy123
    • one year ago
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    you mean \(s(t) = te^t\) ??

  3. zeesbrat3
    • one year ago
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    I suppose, I just copied the question honestly. @IrishBoy123

  4. IrishBoy123
    • one year ago
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    if you do mean: \(\large s(t)=te^t\) then \(\large v(t) = \dot s(t)=\frac{d}{dt}( te^t)\) use product rule and set it to zero to find when the things is at rest

  5. zeesbrat3
    • one year ago
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    so find the derivative?

  6. Michele_Laino
    • one year ago
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    yes!

  7. zeesbrat3
    • one year ago
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    I tried doing what we did but that didn't work, but doing what he just said makes sense. I got 0 as a solution

  8. Michele_Laino
    • one year ago
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    maybe your function is like this: \[\Large s\left( t \right) = t{e^{ - t}}\]

  9. Michele_Laino
    • one year ago
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    sorry, if I compute the first derivative, I got this: \[\Large \frac{{d\left( {t{e^t}} \right)}}{{dt}} = \left( {t + 1} \right){e^t}\]

  10. Michele_Laino
    • one year ago
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    so we have to solve this algebraic equation: \[\Large \left( {t + 1} \right){e^t} = 0\]

  11. zeesbrat3
    • one year ago
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    I got -1 as a solution

  12. Michele_Laino
    • one year ago
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    that's right!

  13. zeesbrat3
    • one year ago
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    Awesome! Thank you for your help!!

  14. Michele_Laino
    • one year ago
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    :)

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