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MathGroup Archive 1996

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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[2]
>
>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[2] 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[17]:=
  Max[D[x - 1, x], 0] /. x -> 2
Out[17]=
  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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