according to the POD, you can create a Math::Spline object with a number of points (as two array refs). You can then evaluate the result for a particular point.

The advantage of this method is that you can locate a point that is on a continuous line but which isn't a point in your data.

This is what I would do:

my $max = [ $x[ 0 ], $y[ 0 ] ];
for my $i ( 1..$#x ) {
  last if $y[ $i ] <= $max[ 1 ];
  $max = [ $x[ $i ], $y[ $i ] ];
}
print "max at ($max->[ 0 ], $max->[ 1 ])\n";
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This code makes two important assumptions: that your data is ordered in the x-axis and that it is really as smooth as you describe it. If neither of these two assumptions hold, the following would be better:

my $max = [ $x[ 0 ], $y[ 0 ] ];
for my $i ( 1..$#x ) {
  $max = [ $x[ $i ], $y[ $i ] ] if $y[ $i ] > $max->[ 1 ];
}
print "max at ($max->[ 0 ], $max->[ 1 ])\n";
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The slope of a line is y = Mx + b, where M is the slope. M is usually (y2 -y1)/(x2 - x1).

I think Pustular Postulant's method is probably faster.

If there is some noise in your input data that causes small peaks to appear, then you need to apply a filter first.

For example, substitute every element by the mean of its predecessor, the element itself and its successor. If this is not enough, try extending the mean to cover more elements around. You can also ponderate the mean calculation so nearer elements have more weight, i.e.:

$fd[$n] = ( 0.25*$d[$n-2] + 0.5*$d[$n-1]
            + 1.0*$d[$n]
            + 0.5*$d[$n+1] + 0.25*$d[$n+2] )
             / (0.25+0.5+1.0+0.5+0.25);
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Not, this is not the right way

What you want probably is to find (to predict) the critic points of the function defined by your sample points. Obtaining the maximum point of the sample is not of much value because what is really interesting in the graph is the curve of the function that fits better your points. Its maximum and minimun points can be (and probably will be) between two given points

You probably need instead

use Math:Derivative;

Clearly your teacher was trying to tell you something with this words. A requisite to be able to find what you want is that your function is continuous

EDIT: Well I see now that a lot of the last messages point to this yet. Your problem is a math problem, not a "sort this array" problem