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Re: Plot of (2 x^2 - x^3)^(1/3)

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  • Subject: [mg112100] Re: Plot of (2 x^2 - x^3)^(1/3)
  • From: Alexei Boulbitch <alexei.boulbitch at>
  • Date: Mon, 30 Aug 2010 06:20:42 -0400 (EDT)

You seem to have defined in the first case your real part with the sign minus at x>2,
but not in the second case, did not you?

I see in Calcul Diff=E9rentiel et int=E9gral, N. Piskounov, Editions 
MIR, Moscou 1970, on p. 210 the graph of (2 x^2 - x^3)^(1/3) with 
negative values for x > 2, something like :

Plot[Piecewise[{{(2 x^2 - x^3)^(1/3), x <= 2}, {-Re[(2 x^2 - 
x^3)^(1/3)],  x > 2}}], {x, -1, 3}]

When I plot this function with :

Plot[(2 x^2 - x^3)^(1/3) // Re, {x, -1, 3}]

I obtain positives values for x > 3. I don't understand why.
Thank you very much for your help !

Alexei Boulbitch, Dr. habil.
Senior Scientist
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ZAE Weiergewan
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