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MathGroup Archive 2009

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Re: Creating a sign chart

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98908] Re: Creating a sign chart
  • From: Helen Read <hpr at together.net>
  • Date: Tue, 21 Apr 2009 05:11:19 -0400 (EDT)
  • References: <gsivd0$9aa$1@smc.vnet.net>
  • Reply-to: HPR <read at math.uvm.edu>

davef wrote:
> Is it possible to render a sign chart in Mathematica 10?
> 
> Typically a sign chart is used with the first and second derivatives
> to identify extrema. I know there are other ways to convey this
> information. However, in my case I need to demonstrate a sign chart by
> means of an illustation. I can create a graphic in Visio and import into
> Mathematica but I would prefer if there were a means of generating such
> a chart directly in Mathematica.
  >
> Something like:
> 
> +++++++++++++++------------

Something like this?

f[x_] = 10 + 108 x - 27 x^2 + 2 x^3


first[x_] := If[f'[x] == 0, x, If[Sign[f'[x]] > 0, "+", "-"]];

second[x_] := If[f''[x] == 0, x, If[Sign[f''[x]] > 0, "+", "-"]];


Labeled[Row[Table[first[x], {x, 0, 10, 1/2}]], "First derivative"]


Labeled[Row[Table[second[x], {x, 0, 10, 1/2}]], "Second derivative"]

-- 
Helen Read
University of Vermont


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