1. §2.8. Derivative functions

10. Higher derivative functions
From the mathematical point of view, the derivative function of a given function is a function. It has its own derivative function. So differentiation can be applied to a derivative function over and over. That is, we can take derivatives of derivatives.

13. Question: Why do we need to apply
differentiation over and over for a given
function? The reason is very simple. We want
to obtain the information on the given function
using the information from derivative functions.
f  would provide some key information on f
but not complete information on f. f  and f 
together gives us most information of f. But it’s
still not complete. In general, to get the complete
information of f, we have to consider all its
higher derivative functions.

16. Comment:
If y = f(t) is the position function of an object that
moves in a straight line, then
velocity v(t) = f (t)
acceleration a(t) = f (t) = v (t)
jerk j(t) = f (t) = a (t)
Note: A large Jerk means that a sudden change in a(t) , which causes an abrupt movement