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:
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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;
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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