have you tried solving your problem on a spreadsheet (Excel or Calc from OO.org) first?

Insert the data on a table and add colums for the first and the second derivates (you can find some formulas to do it below), then create an X-Y graph showing Y, Y' and Y'' so you could visualize and understand what other monks have suggested you about looking for changing signs on the second derivates.

Coding a subrutine in perl to solve the problem and others similar will be much easier then. 

      X         Y        Y'=(Y[n+1]-Y[n-1])/(X[n+1]-X[n-1])
                                      Y''=(Y'[n+1]-Y'[n-1])/(X[n+1]-X[
+n-1])
      4.1330 4580.87             
      4.1470 4522.75     -1328.56
      4.1600 4545.00     -7791.65     -935707.98
      4.1730 4320.17    -25656.96    -1544908.57
      4.1870 3852.26    -49504.19    -1396364.62  -
      4.2000 2983.56    -63358.81       59518.52  +
      4.2130 2204.93     -47956.7     1368481.22
      4.2270 1688.73    -26409.81     1302338.03
      4.2400 1491.87    -12793.58      687964.39
      4.2530 1356.09     -8522.74      246232.62
      4.2670 1261.75      -6145.3       120543.1
      4.2800 1190.17     -5268.08       99532.76
      4.2930 1124.78     -3557.44      180758.68
      4.3070 1094.12      -387.59      357928.14
      4.3200 1114.32      6106.62      533914.53
      4.3330 1252.89     13494.19      473482.01
      4.3470 1478.66     18890.63      334228.18
      4.3600 1762.94     22518.35       61078.35  +
      4.3730 2064.14     20478.67     -278669.88  -
      4.3870 2315.86     14994.26     -533957.74
      4.4000 2468.98      6061.81     -715688.03
      4.4130 2473.47     -3613.63     -574250.77
      4.4270 2371.42     -9442.96     -274812.86  -
      4.4400 2218.51    -11033.58       93502.85  +
      4.4530 2084.54     -7011.89      376399.97
      4.4670 2029.19      -870.78       468240.9
      4.4800 2061.03      5630.62      455004.27
      4.4930 2175.58     10959.33      278503.96
      4.5070 2356.93     13150.22       13708.45  +
      4.5200 2530.64     11329.46      -316569.8  -
      4.5330 2651.50      4919.41     -526292.81
      4.5470 2663.46     -2880.44     -563985.17
      4.5600 2573.73    -10308.19     -476770.66
      4.5730 2395.45    -15276.48     -346338.56
      4.5870 2161.26    -19659.33      -286611.8
      4.6000 1864.65       -23015      -18659.54  -
      4.6130 1562.87    -20144.48      218052.13  +
      4.6270 1320.75    -17127.59      195150.31
      4.6400 1100.43    -14875.42      287534.19
      4.6530  933.99      -9651.7      387333.91
      4.6670  839.83     -4417.41      369091.59
      4.6800  814.72       313.77      341683.76
      4.6930  847.99      4466.37      298057.93
      4.7070  935.31      8361.33      382671.47
      4.7200 1073.75      14798.5      519444.44
      4.7330 1320.07     21866.89      519764.75
      4.7470 1664.15     28832.15      506969.93
      4.7600 2098.54     35555.08
      4.7730 2588.58

[download]

In reply to Re^3: Any idea for predicting the peak points in the graph by perl by salva
in thread Any idea for predicting the peak points in the graph by perl by Anonymous Monk

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