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Re: Plotting f = Function[x,expr] and f[x_] := expr

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92441] Re: Plotting f = Function[x,expr] and f[x_] := expr
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Tue, 30 Sep 2008 21:53:33 -0400 (EDT)
  • References: <gbt2oo$lbo$1@smc.vnet.net>

E. Martin-Serrano schrieb:
> Hi,
>
> Why this apparent estrange behavior while plotting  functions  under the
> formats f[x_] := -20 x^3 + 3 x^5 and f = Function[x, -20 x^3 + 3 x^5]?, 
>
> In particular  the second derivative f ''[x]  for -20 x^3 + 3 x^5 fails to
> render the shame shape in following examples . Please, see below: 
>
> ------------------------------------------------------
>
>  
>
> This works as expected 
>
>  
>
> In[1]:= Clear[f, x]
>
> f[x_] := -20 x^3 + 3 x^5
>
> f[x]
>
> f'[x]
>
> f''[x]
>
>  
>
> In[6]:= Plot[f[x], {x, -2  Pi, 2  Pi}, PlotStyle -> Red]
>
> In[7]:= Plot[f'[x], {x, -2  Pi, 2  Pi}, PlotStyle -> Green]
>
> In[8]:= Plot[f''[x], {x, -2  Pi, 2  Pi}, PlotStyle -> Blue]
>
> In[9]:= Plot[{f[x], f'[x], f''[x]}, {x, -2  Pi, 2  Pi}, 
>
>  PlotStyle -> {Red, Green, Blue}, 
>
>  PlotRange -> {{-6.28318, 6.27681}, {-14129, 14084}}]
>
>  
>
> --------------------------------------------
>
>  
>
> This do work too
>
>  
>
> In[10]:= Clear[f, x]
>
> f = Function[x, -20 x^3 + 3 x^5]
>
> f''[x]
>
> tp = Table[N@{x, %}, {x, -2 Pi, 2 Pi, .001}];
>
> llp = ListLinePlot[tp]
>
> fgif = FullGraphics[llp] // InputForm;
>
>  
>
> --------------------------------------
>
>  
>
> This does not (The second derivative is plotted pretty flat)
>
>  
>
> In[16]:= Clear[f, x]
>
> f = Function[x, -20 x^3 + 3 x^5];
>
> f[x]
>
> f'[x]
>
> f''[x]
>
>  
>
> In[21]:= Plot[f[x], {x, -2  Pi, 2  Pi}, PlotStyle -> Red]
>
> In[22]:= Plot[f'[x], {x, -2  Pi, 2  Pi}, PlotStyle -> Green]
>
> In[23]:= Plot[f''[x], {x, -2  Pi, 2  Pi}, 
>
>  PlotStyle ->  Blue] (* here seems to be the problem *)
>
> In[24]:= Plot[{f[x], f'[x], f''[x]}, {x, -2  Pi, 2  Pi}, 
>
>  PlotStyle -> {Red, Green, Blue}, 
>
>  PlotRange -> {{-6.28318, 6.27681}, {-14129, 14084}}]
>
>  
>
>  
>
> I need the format : f = Function[x, -20 x^3 + 3 x^5]
>
>  
>
> E. Martin-Serrano
>

I don't see a difference in any of your plots between f[x_]=... and
g=Function[x, ...]

Gruss Peter
-- 
==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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