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