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

*To*: mathgroup at smc.vnet.net*Subject*: [mg112100] Re: Plot of (2 x^2 - x^3)^(1/3)*From*: Alexei Boulbitch <alexei.boulbitch at iee.lu>*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 Material Development IEE S.A. ZAE Weiergewan 11, rue Edmond Reuter L-5326 CONTERN Luxembourg Tel: +352 2454 2566 Fax: +352 2454 3566 Mobile: +49 (0) 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu www.iee.lu -- This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you are not the intended recipient and have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal from your system. Thank you for your co-operation. __________ Information from ESET NOD32 Antivirus, version of virus signature database 5407 (20100829) __________ The message was checked by ESET NOD32 Antivirus. http://www.eset.com