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;

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
____________________________________________________________________

```

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