The second derivative can tell us exactly the same kinds of things about the first derivative, that the first derivative tells us about the original function.What are some real world uses of using a derivative of a derivative (in general)? I get what a derivative can tell us but I am fuzzy on what a derivative of a derivative can tell us.
Suppose a particle is moving on a path described by y = f(x).Thanks for the help. That clears things up for me. As a late life goal I've taken on mathematics as a hobby. As I have found out it helps me to know what something is telling me rather than calculating numbers for the sake of calculating numbers. My lesson yesterday was calculating 2nd,3rd,.... derivatives. The whole lesson I was thinking "Ok but what is this telling me?". Thanks again.