MHB Advanced Functions Average vs. Instantaneous velocity

[Wild ownz al]

What do the average velocities on the very short time intervals [2,2.01] and [1.99,2] approximate? What relationship does this suggest exist between a velocity on an interval [a,b] and a velocity near t=a+b/2 for this type of polynomial?

 

[HOI]

That looks very much like a question that is asking you to think about what happens when you calculate an "average value" in order to lead you think about what the phrase "instantaneous velocity" could mean! You need to do it, not have someone else do it for you!
If at time t= 1.99 you are at point 2 and at time 2 you are position 2.01, you have moved from 2 to 2.01 so have moved a distance 2.01- 2= 0.01. And you did that in time interval 2- 1.99= 0.01.

If you move a distance 0.01 (km, say) in 0.01 (hours, say) what was your average velocity in that time interval?

Since velocity, in this way, is "the distance moved in a given time interval divided by the length of that time interval", do you see the problem with even defining "velocity at a given interval"?