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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