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

• To: mathgroup at smc.vnet.net
• Subject: [mg92445] RE: Plotting f = Function[x,expr] and f[x_] := expr
• From: "E. Martin-Serrano" <eMartinSerrano at telefonica.net>
• Date: Tue, 30 Sep 2008 21:54:17 -0400 (EDT)
• References: <gbt2oo\$lbo\$1@smc.vnet.net> <48E23533.8070203@gmail.com>

```Hi,

Perhaps the problem is in version 6.0.1. The following is my result. Anybody
still in 6.0.1?

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

Out[3]= Function[x, -20 x^3 + 3 x^5]
In[4]:= Plot[g''[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue] ===
Plot[f''[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue]

Out[4]= False

-----Original Message-----
From: Szabolcs Horv=E1t [mailto:szhorvat at gmail.com]
Sent: martes, 30 de septiembre de 2008 15:18
To: E. Martin-Serrano
Subject: [mg92445] Re: Plotting f = Function[x,expr] and f[x_] := expr

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 same 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 does 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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