§2.8. Derivative functions

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.

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.

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