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

• To: mathgroup at smc.vnet.net
• Subject: [mg92425] Re: Plotting f = Function[x,expr] and f[x_] := expr
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 30 Sep 2008 21:50:32 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <gbt2oo\$lbo\$1@smc.vnet.net>

```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 shame shape in following examples . Please, see below:

FWIW, to me as well as for Mathematica 6.0.3 on 64-bit Intal Mac OS X
10.5.5, the plots are identical in each case.

In:=

Clear[f, x]
f[x_] := -20 x^3 + 3 x^5
pp1 = Plot[f[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Red]
pp2 = Plot[f'[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Green]
pp3 = Plot[f''[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue]
pp4 = Plot[{f[x], f'[x], f''[x]}, {x, -2 Pi, 2 Pi},
PlotStyle -> {Red, Green, Blue},
PlotRange -> {{-6.28318, 6.27681}, {-14129, 14084}}]

Clear[f, x]
f = Function[x, -20 x^3 + 3 x^5];
p1 = Plot[f[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Red]
p2 = Plot[f'[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Green]
p3 = Plot[f''[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue]
p4 = Plot[{f[x], f'[x], f''[x]}, {x, -2 Pi, 2 Pi},
PlotStyle -> {Red, Green, Blue},
PlotRange -> {{-6.28318, 6.27681}, {-14129, 14084}}]

p1 === pp1
p2 === pp2
p3 === pp3
p4 === pp4

Out= True

Out= True

Out= True

Out= True

In:= \$Version

Out= "6.0 for Mac OS X x86 (64-bit) (May 21, 2008)"

Regards,
-- Jean-Marc

```

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