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eroshea

  • 2 years ago

find all the critical point of f(x) = 3x^(5/3) - 15x^(2/3)

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  1. terenzreignz
    • 2 years ago
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    Critical points are points where the derivative is zero.

  2. terenzreignz
    • 2 years ago
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    Of course, differentiate first :)

  3. eroshea
    • 2 years ago
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    ok.. i got x=0, x=2

  4. terenzreignz
    • 2 years ago
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    let's see.... \[\Large \frac{d}{dx}\left(3x^{\frac53}-15x^{\frac23}\right)=5x^{\frac23}-10x^{-\frac13}\]

  5. eroshea
    • 2 years ago
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    is my answer correct?

  6. terenzreignz
    • 2 years ago
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    Try 0. the derivative doesn't exist, because you have... \[\Large 5x^{\frac23}-10x^{-\frac13}=5x^{\frac23}-\frac1{10x^{\frac13}}\] an x in the denmoinator.

  7. eroshea
    • 2 years ago
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    so that will be disregarded right? so i will have 2 for the value of x

  8. terenzreignz
    • 2 years ago
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    so yes, that is a critical point (sorry, I forgot to mention that points where the derivative does not exist are also critical points)

  9. eroshea
    • 2 years ago
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    owh.. i see

  10. eroshea
    • 2 years ago
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    so what next? how will i graph?

  11. terenzreignz
    • 2 years ago
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    Hang on, I'm not sure about the 2 yet. Let's try equating the derivative to zero. \[\Large0=5x^{\frac23}-\frac1{10x^{\frac13}}\]\[\Large5x^{\frac23}=\frac1{10x^{\frac13}}\]\[\Large5x^{\frac23}\cdot 10x^{\frac13}=1\]\[\Large50x=1\] Are you sure it's x = 2? :P

  12. eroshea
    • 2 years ago
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    can you factor out 5x^(1/3) from 5x^(2/3)−10x^(−1/3)?

  13. terenzreignz
    • 2 years ago
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    You can... but why would you do that?

  14. eroshea
    • 2 years ago
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    what will be the answer if you would factor out that one? 5x^(-1/3) i got a little confused

  15. terenzreignz
    • 2 years ago
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    I think it leads nowhere :)

  16. eroshea
    • 2 years ago
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    owh.. lol.. so x = 1/50?

  17. terenzreignz
    • 2 years ago
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    yeah :)

  18. eroshea
    • 2 years ago
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    what is the answer if i would take out 5x^(-1/3) from 5x^(2/3) i really am confused on what will be the outcome

  19. terenzreignz
    • 2 years ago
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    Hang on, I may have made a mistake.

  20. terenzreignz
    • 2 years ago
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    Okay... apparently, 2 was right.

  21. terenzreignz
    • 2 years ago
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    sorry.

  22. eroshea
    • 2 years ago
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    yehey :D so.. what to do next ?

  23. terenzreignz
    • 2 years ago
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    just like that? You're not going to ask me where my error was? :/ You didn't spot it yet... means you may well commit the same... come on, a little challenge :P

  24. terenzreignz
    • 2 years ago
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    \[\Large0=5x^{\frac23}-\frac1{10x^{\frac13}}\] I should not have put 10 in the denominator. Big mistake. Correct would be \[\Large0=5x^{\frac23}-\frac{10}{x^{\frac13}}\color{green}\checkmark \]

  25. eroshea
    • 2 years ago
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    you shouldn't include 10 in the denominator.. it should be on the numerator :D

  26. terenzreignz
    • 2 years ago
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    yeah that :) sorry about that. I might be getting drowsy.

  27. terenzreignz
    • 2 years ago
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    And as far as I know... we're done.

  28. eroshea
    • 2 years ago
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    that's ok.. :))

  29. terenzreignz
    • 2 years ago
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    We already have the critical points.

  30. eroshea
    • 2 years ago
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    then how to graph?

  31. terenzreignz
    • 2 years ago
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    whoops... you'll need to consult one of the big guys for that :3 I'm rather terrible at graphing, you see...

  32. eroshea
    • 2 years ago
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    owh.. that'll be okay then.. thanks for the help! :D

  33. terenzreignz
    • 2 years ago
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    No problem :)

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