Find the Peak of a Curve Defined by Points

[davidco2]

I have a curve defined by some points.
These points represent the pixel brightness on the image sensor

For example get these values:
5 14 60 111 100 37

Where is the brightness peak? Somewhere between pixel 4 and 5... ~4,3

Is there a method to determine this? Something with a name or do you have an idea?

 

[HallsofIvy]

There is no way to "determine" from, discrete values, where a curve might peak. Certainly, It would be possible to construct a smooth curve through those points which would have a maximum value of 111. Since there is no reason, here, to think there are values larger than 111, that would seem most reasonable to me. But it would be just as possible to construct a smooth function giving those values that would have a "peak" of any number you wished to give between, say, 5 and 14. Do you have any information in addition to what is given there?

 

[davidco2]

This is a cross-section of the laser line and if the center of the line is on 4.3 (numerating above pixels as 1-6) the peak would be over 111
If I draw a graph in Excel using these values and set curve to smooth, the peak is drawn somewhere around 4.3