Maximizing Accuracy: Comparing Average and Instantaneous Velocity Calculations

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OrbitalPower
Instead of finding the average velocity http://theoryx5.uwinnipeg.ca/physics/onedim/node3.html , could you also find the instantaneous velocity of two points of a function and divide by 2 (or something similar, it may not be instantaneous).
 
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If you know the initial and final velocity then yes the average is the sum of the two velocities divided by two.