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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20121129110446.BF9AD688F@smc.vnet.net>

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) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Color according to concavity***From:*Sergio Miguel Terrazas Porras <sterraza@uacj.mx>