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Simplifying a cubic

  1. Oct 18, 2014 #1
    I need to find the local extrema of

    [tex]\pi r^2(\frac{16}{(r+.5)^2}-1)[/tex]

    which I derived and simplified to

    [tex]\frac{16 \pi r}{(r+.5)^3}=2 \pi r[/tex]

    which simplifies to [tex]\frac {16 \pi r}{2 \pi r}=(r+.5)^3[/tex]

    The radius cannot be zero, so I simplified [tex]8=(r+.5)^3[/tex]

    I used the binomial theorem and more algebra to obtain


    Now I am unsure of how to simplify the cubic. Normally I would use rational roots, but I don't know how to do that with an integer constant. I need either a method of simplifying this cubic or a place where I could have simplified the derivative better.
  2. jcsd
  3. Oct 18, 2014 #2
    8 = (r+0.5)3 , why not to take 3rd root ?
  4. Oct 18, 2014 #3
    Oh my god, I can't believe I missed that.
    Thanks, I guess.
  5. Oct 18, 2014 #4


    Staff: Mentor

    ... which you differentiated, simplified, and then set to zero.
  6. Oct 18, 2014 #5
    ciuba,ciuba you messed it up more than once
  7. Oct 18, 2014 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Try the full-fledged "rational root theorem' as described in http://en.wikipedia.org/wiki/Rational_root_theorem --- it works. However, you need to convert to integer coefficients throughout.
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