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Re: Color according to concavity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128851] Re: Color according to concavity
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 30 Nov 2012 05:57:45 -0500 (EST)
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On Nov 29, 2012, at 6:04 AM, Sergio Miguel Terrazas Porras <sterraza at uacj.mx> wrote:
>
> I want to plot a function with the color of the parts of the curve according to concavity, say Red when concve down an blue when concave up.
>
> I can do it by brute force, finding whwn the second derivative is cero, and then finding the sign of it in the different intervals, etc. This for particular examples.
>
> But, is there a way to use the second derivative as part of a ColorFunction, or something like that?

One might think the following would work, but it doesn't. (The color erroneously remains constant after the local minimum.)

  f[x_] := x^2 - x^3 + 10 x
  Plot[f[x], {x, -5, 5},
        ColorFunction -> Function[{x, y}, If[f''[x] < 0, Red, Blue]]
      ]

---
Murray Eisenberg                                    
murray at math.umass.edu
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
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