Re: Problems with differentiating Piecewise functions
- To: mathgroup at smc.vnet.net
- Subject: [mg86970] Re: Problems with differentiating Piecewise functions
- From: "David Park" <djmpark at comcast.net>
- Date: Thu, 27 Mar 2008 08:20:39 -0500 (EST)
- References: <fsd6ph$9hb$1@smc.vnet.net>
Although you can often get away with argumentless definitions, I think it is
always better to define functions with argument patterns.
pw1[x_] = Piecewise[{{x^2, x <= 0}, {x, x > 0}}]
Then you can get the derivative by simply writing
pw1'[x]
The derivative is undefined at x == 0 so Mathematica is correct.
--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
"hlovatt" <howard.lovatt at gmail.com> wrote in message
news:fsd6ph$9hb$1 at smc.vnet.net...
> If I set up a piecewise function and differentiate it:
>
> In[112]:= pw1 = Piecewise[{{x^2, x <= 0}, {x, x > 0}}]
>
> Out[112]= \[Piecewise] {
> {x^2, x <= 0},
> {x, x > 0}
> }
>
> In[113]:= pw1 /. x -> 0
>
> Out[113]= 0
>
> In[114]:= pw1d = D[pw1, x]
>
> Out[114]= \[Piecewise] {
> {2 x, x < 0},
> {1, x > 0},
> {Indeterminate, \!\(\*
> TagBox["True",
> "PiecewiseDefault",
> AutoDelete->False,
> DeletionWarning->True]\)}
> }
>
> In[115]:= pw1d /. x -> 0
>
> Out[115]= Indeterminate
>
> Then at the joins between the pieces I get Indeterminate values,
> because the limit x <= 0 has become x < 0 after differentiation. Does
> anyone know a solution to this problem?
>
> Thanks,
>
> Howard.
>