Re: How to get the maximums of a curve

• To: mathgroup at smc.vnet.net
• Subject: [mg66865] Re: How to get the maximums of a curve
• From: "Valeri Astanoff" <astanoff at yahoo.fr>
• Date: Fri, 2 Jun 2006 04:08:27 -0400 (EDT)
• References: <e5js8v\$e44\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Simon,

Here is a quick DIY way to find local maximums (just an example) :

In[1]:=data={{0,1.09},{1,2.01},{2,1.92},{3,1.18},{4,0.29},
{5,0.109},{6,0.801},{7,1.66},{8,2.064},{9,1.47},
{10,0.518},{11,0.0379},{12,0.471},{13,1.514},{14,2.017},
{15,1.65}}; xmin=0; xmax=15;

In[2]:=f=Interpolation[data];

In[3]:=ListPlot[Table[{x,f[x]},{x,xmin,xmax,0.1}] ,PlotJoined->True]

Out[3]= - Graphics -

In[4]:=t=Table[FindRoot[f'[x] == 0,{x,u}],{u,xmin,xmax,0.1}];
[warning interpolation messages...]

In[5]:={x,f[x]} /.
Select[Union[t, SameTest -> (Abs[(x/.#2)-(x/.#1)]<10^-5&)] ,
f''[x/.#] < 0 && xmin < (x /. #) < xmax&]

Out[5]={{1.37679,2.07527},{7.99549,2.06401},{14.1378,2.02555}}

hth

V.Astanoff

```

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