Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: how to show for what values the function is

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104099] Re: how to show for what values the function is
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 19 Oct 2009 07:11:51 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

f[x_, m_] = m*Log[x]/2^m + (1 - x^m)/(1 + x)^m;

dfdx[x_, m_] = FullSimplify[D[f[x, m], x]];

Plot3D[f[x, m],
 {x, 1, 20}, {m, -2, 5}, 
 PlotRange -> {-1/2, 1},
 ClippingStyle -> None,
 ColorFunction -> Function[{x, m, z},
   If[Re[dfdx[x, m]] > 0, Lighter[Blue, .6], Red]],
 ColorFunctionScaling -> False,
 Mesh -> 10,
 PlotPoints -> 75]

Plot3D[{dfdx[x, m], 0},
 {x, 1, 20}, {m, -2, 5}, 
 PlotRange -> {-1/16, 1/16},
 ClippingStyle -> None,
 PlotStyle -> {Automatic,
   Directive[Red, Opacity[.75]]}]

ContourPlot[dfdx[x, m],
 {x, 1, 20}, {m, -2, 5}]


Bob Hanlon

---- JEZUS <barefoot1980 at gmail.com> wrote: 

=============

how to show

that for what values of m, the function

f(x) = m * log(x) / 2^m + (1-x^m) / (1+x)^m

is increasing/decreasing. That for what values of m, df/dx > 0 for all
x>=1, ....

here, x >= 1


it looks like the (i am not sure):


df/dx > 0 for 0 < m <=3

df/dx < 0 for m < 0

df/dx < 0 for m > 0



  • Prev by Date: Re: GraphicsGrid crashes front end?
  • Next by Date: Re: GraphicsGrid crashes front end?
  • Previous by thread: Re: mathematica@linux, character encoding
  • Next by thread: options for VectorPlot in version 7 vs VectorFieldPlot in version 6