Re: Graphing Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg22543] Re: [mg22476] Graphing Functions
- From: Bojan Bistrovic <bojanb at python.physics.odu.edu>
- Date: Thu, 9 Mar 2000 03:24:28 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
> As a relative novice in Mathematica, I need help with a very basic > problem involving the graphing of a certain function. > > The function in question is: > > x^(1/3) - > x^(2/3). > > The plotting function Plot[f, xmin, xmax] seems unable to deal with cube > roots of negative fractional real numbers. > > Please let me know how I can obtain a plot of the above function over > the real number line from say, from x = -10 to x = 10. > > Thank you. > > Julian > Using the identity x=Exp[Log[x]] you have x^(1/3) - x^(2/3)= Exp[1/3 Log[x] ] - Exp[2/3 Log[x]] which for negative numbers becomes Abs[x]^(1/3) Exp[I Pi/3] - Abs[x]^(2/3) Exp[2 I Pi/3] or Abs[x]^(1/3) (1 + I Sqrt[3])/2 - Abs[x]^(2/3) (-1 + I Sqrt[3])/2 which in general ISN'T real for x<0 so you have to use 3D plots. Bye, Bojan -- --------------------------------------------------------------------- Bojan Bistrovic, bojanb at jlab.org Old Dominion University, Norfolk VA & Jefferson Lab, Newport News, VA ---------------------------------------------------------------------