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

*To*: mathgroup at smc.vnet.net*Subject*: [mg92400] Re: Plotting f = Function[x,expr] and f[x_] := expr*From*: "Szabolcs HorvÃt" <szhorvat at gmail.com>*Date*: Tue, 30 Sep 2008 21:45:57 -0400 (EDT)*References*: <gbt2oo$lbo$1@smc.vnet.net> <48E23533.8070203@gmail.com>

I cannot test this on 6.0.1, but here's a guess: Try Plot[Evaluate[g''[x]], {x, -2Pi, 2Pi}] or Plot[g''[x], {x, -2Pi, 2Pi}, Evaluated -> True]. Do they produce the correct result? The Plot function of Mathematica 6 has the nasty habit of silently ignoring errors. I use On[General::plnr] in init.m, which partially restores the behaviour of Mathematica <= 5.2. While the Plot::plnr message was annoying to many users, I wouldn't call it completely useless ... On Tue, Sep 30, 2008 at 16:32, E. Martin-Serrano <eMartinSerrano at telefonica.net> wrote: > > 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 HorvÃ¡t [mailto:szhorvat at gmail.com] > Sent: martes, 30 de septiembre de 2008 15:18 > To: E. Martin-Serrano > Subject: 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 > >