Re: Labelling a plot with maximum

• To: mathgroup at smc.vnet.net
• Subject: [mg105175] Re: [mg105146] Labelling a plot with maximum
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Mon, 23 Nov 2009 06:52:59 -0500 (EST)

```Hi, Shalin,
try this. Alexei

jinc[x_] := BesselJ[1, 2 \[Pi] x]/(2 \[Pi] x);
f[x_, \[CapitalDelta]_] :=
4 Abs[jinc[x + \[CapitalDelta]] - jinc[x - \[CapitalDelta]]]^2;

Manipulate[DynamicModule[{nmx},

nmx = Dynamic[NMaximize[f[x, \[CapitalDelta]], x][[2, 1, 2]]];

Column[{Row[{Style[
"\!\(\*SubscriptBox[\"x\", \"max\"]\)=\[PlusMinus]", Red, Bold,
18], Style[nmx, Red, Bold, 18]}],
Plot[f[x, \[CapitalDelta]], {x, -1.22, 1.22},
PlotRange -> {{-0.5, 0.5}, {0, 1.5}}]}]], {\[CapitalDelta],
0.125, 0.5}]

Hi everyone,

I am very new to Mathematica. I wish to prepare a figure and a movie
where the maximum of the plot is labelled on the figure.

I am using Manipulate to animate a function as shown below:

jinc[x_] := BesselJ[1, 2 \[Pi] x]/(2 \[Pi] x);
f[x_, \[CapitalDelta]_] :=
4 Abs[jinc[x + \[CapitalDelta]] - jinc[x - \[CapitalDelta]]]^2;
Manipulate[
Plot[f[x, \[CapitalDelta]], {x, -1.22, 1.22},
PlotRange -> {{-0.5, 0.5}, {0, 1.5}}], {\[CapitalDelta], 0.125,
0.5}]

I find the maximum for different values of Delta using:
Manipulate[
NMaximize[f[x, \[CapitalDelta]], x], {\[CapitalDelta], 0.125,
0.5}]

by NMaximize on (say) top-left of the Plot generated by the first
Manipulate above? The plot will look  neat if I can place a marker at
the X-position of maximum.

Also, I wish to have a Motion-JPEG compressed quicktime mov file
exported from this manipulate. How can that be achieved?

thanks in advance for any help.
Shalin

--
Alexei Boulbitch, Dr., habil.
Senior Scientist

IEE S.A.
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Luxembourg

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