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Re: Color according to concavity

Bob Hanlon got the trick by setting ColorFunctionScaling to False. But one
thing I notice is that the curve no longer has antialiasing.

I don't know if the following qualifies as brute force, but it is rather
intuitively simple with Presentations and one obtains better looking curves
with antialiasing.

<< Presentations` 

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

 {Red, Draw[f[x], {x, -5, 5}, RegionFunction -> (f''[#] > 0 &)],
  Blue, Draw[f[x], {x, -5, 5}, RegionFunction -> (f''[#] < 0 &)]},
 Frame -> True, AspectRatio -> 1/2] 

For Bob Hanlon's example:

g[x_] := Sin[x] Cos[2 x]

 {Red, Draw[g[x], {x, -5, 5}, RegionFunction -> (g''[#] > 0 &)],
  Blue, Draw[g[x], {x, -5, 5}, RegionFunction -> (g''[#] < 0 &)]},
 Frame -> True, AspectRatio -> 1/GoldenRatio]

Or do it with a Show.

David Park
djmpark at 

From: Murray Eisenberg [mailto:murray at] 

On Nov 29, 2012, at 6:04 AM, Sergio Miguel Terrazas Porras
<sterraza at> 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
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower            phone 413 549-1020 (H)
University of Massachusetts                               413 545-2838 (W)
710 North Pleasant Street                         fax   413 545-1801
Amherst, MA 01003-9305

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