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Stuck with this cubic equation

  1. Feb 12, 2017 #1
    1. The problem statement, all variables and given/known data
    Refer to attached image. Please help. It's due tomorrow.

    2. Relevant equations
    Doesn't state

    3. The attempt at a solution
    Refer to attached image
     

    Attached Files:

  2. jcsd
  3. Feb 12, 2017 #2
    Hi Ameer:
    I also found two values for x for which f'=0, but my values are different than yours. Might you have copied the problem incorrectly?

    Regards,
    Buzz
     
  4. Feb 12, 2017 #3

    Mark44

    Staff: Mentor

    Since the problem is shown as an image, I don't see how it could have been copied incorrectly. I'm wondering if there is a typo in the problem itself. I too get two values for critical points. The only way that there will be only one solution for x in solving for f'(x) = 0, is the the discrimant has to be zero. IOW, ##4c^2 - 24m = 0##. If ##c^2 = 8m##, the discriminant is ##32m - 24m = 8m##.

    One comment about the OP's work: if ##c^2 = 8m##, then it's not necessarily true that ##c = 2\sqrt{2m}##. Corrected, it would be ##c = \pm 2\sqrt{2m}##.
     
  5. Feb 12, 2017 #4

    Mark44

    Staff: Mentor

  6. Feb 12, 2017 #5
    I'm sorry. I'll check your link and won't post it like I did the next time. Thank you
     
  7. Feb 12, 2017 #6
    Hi people. I emailed my teacher and he said that : CĀ² = 6M

    There was a typing error on the page.
     
  8. Feb 12, 2017 #7
  9. Feb 12, 2017 #8
    Got it, thanks guys
     
  10. Feb 12, 2017 #9

    Mark44

    Staff: Mentor

    It's a lot simpler to NOT substitute for c^2 until later.
    If f'(x) = 0, then ##x = \frac{2c \pm \sqrt{4c^2 - 24m}}{12}##. Now, replace ##c^2## with 6m.
     
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