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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92374] Plotting f = Function[x,expr] and f[x_] := expr
  • From: "E. Martin-Serrano" <eMartinSerrano at telefonica.net>
  • Date: Tue, 30 Sep 2008 07:32:56 -0400 (EDT)

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}}]

 

 

I need the format : f = Function[x, -20 x^3 + 3 x^5]

 

E. Martin-Serrano




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