Re: Differentiating Piecewise Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg14825] Re: Differentiating Piecewise Functions*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Wed, 18 Nov 1998 01:29:30 -0500*Organization*: University of Western Australia*References*: <72e2q0$oi3@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Des Penny wrote: > I've got a problem understanding how Mathematica finds the derivative of > a piecewise function. > > Consider the following: > In[1]:= > Clear[f] > f[x_ /; (x<0)]:=x; > f[x_ /; (x>=0 && x<3)]:=Sin[x]; > f[x_ /; (x>=3)]:=x-4; Not an answer to your question -- but another approach to your problem is to use FunctionInterpolation: g = FunctionInterpolation[f[x], {x, -5, 10}, InterpolationPoints -> 30, MaxRecursion -> 8]; Plot[Evaluate[{g[x], g'[x]}], {x, -5, 10}, PlotStyle -> {Hue[0], Hue[1/3]}]; Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________