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