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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92409] Re: Plotting f = Function[x,expr] and f[x_] := expr
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Tue, 30 Sep 2008 21:47:35 -0400 (EDT)
  • Organization: University of Bergen
  • References: <gbt2oo$lbo$1@smc.vnet.net>

E. Martin-Serrano wrote:
> 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}}]
> 

The two commands produce the same plot with Mathematica 6.0.3:

In[1]:= f[x_] := -20 x^3 + 3 x^5

In[2]:= g = Function[x, -20 x^3 + 3 x^5]

Out[2]= Function[x, -20 x^3 + 3 x^5]

In[3]:= Plot[g''[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue] ===
  Plot[f''[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue]

Out[3]= True


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