What Are the Key Differences Between Derivatives and Averages in Research?

[PrudensOptimus]

I'm doing a s. research paper on D vs A.

Anyone give some insights what I can talk about?? I was thinking of comparing how inacurate averages are in some situations. But lack of math talents I don't know how to start:\

 

[MathematicalPhysicist]

Originally posted by PrudensOptimus
I'm doing a s. research paper on D vs A.

Anyone give some insights what I can talk about?? I was thinking of comparing how inacurate averages are in some situations. But lack of math talents I don't know how to start:\

let's see if my physics talents exist
the derevative of a body can give you the precise velocity at a particular time while average doesn't give you this preciseness.



if I am wrong, correct me.

 

[Digit]

Derivatives and averages are almost opposites.
At the bottom, derivatives subtract, averages add.

 

[HallsofIvy]

Originally posted by Digit
Derivatives and averages are almost opposites.
At the bottom, derivatives subtract, averages add.

That looks very deep but I have absolutely no idea what it means!


One thing to note is that derivatives are limits of averages.

Also the mean value theorem asserts that when you average over an interval, there always exist some point in that interval where the derivative is exactly equal to the average.

 

[uart]

Originally posted by Digit
Derivatives and averages are almost opposites.
At the bottom, derivatives subtract, averages add.

Not exactly sure what you're saying in the second sentence but I certainly agree about averages and derivatives being essentually opposites.

Time domain averages are simply the time integral divided by the total time. Integrals of course are anti-derivatives and hence the sense in which the two proposed things are opposites. I don't really see how they are even comparible.