       Re: question

• To: mathgroup at smc.vnet.net
• Subject: [mg4098] Re: question
• From: rhall2 at umbc.edu (hall robert)
• Date: Tue, 4 Jun 1996 02:17:59 -0400
• Organization: University of Maryland, Baltimore County
• Sender: owner-wri-mathgroup at wolfram.com

```In article <4obem1\$na9 at dragonfly.wolfram.com>,
Zvi Wiener  <mswiener at pluto.mscc.huji.ac.il> wrote:

>I think there is something strange in the following lines:
>
>In[]:=
>yy[x_]:=Max[ x-1, 0];
>D[ yy[x], x]/.x->2
>
>Out[]:=
>   (0,1)
>Max     [0, 1]
>
>
>However
>
>In[]:=
>D[Sin[x], x]/.x->2
>
>Out[]:=
>Cos
>
>Of course the function Max is not everywhere differentiable, but I would
>expect to get something like step function and at least value 1 at the point
>where the function is smooth.
>
>How I can avoid the trouble of defining the derivative of Max?  Is the
>problem only with evaluating the expressoin before differentiating or it is
>general property of dealing with not every where differentiable functions?

According to The Book, Mathematica tries to find an explicit value
for a derivative. The derivative of the sine is the cosine, and
Cos is an explicit value. The derivative of Max[] has no
corresponding function, so Mathematica treats it as it would
g[x - 1, 0]. Try the following:

In:=
Max[D[x - 1, x], 0] /. x -> 2
Out=
1

This allows Mathematica to take a derivative it can find a value for.

--
Bob Hall            | "Know thyself? Absurd direction!
rhall2 at gl.umbc.edu  |  Bubbles bear no introspection."  -Khushhal Khan Khatak

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