This is a question about understanding the concept of curvature. Firstly, what exactly is curvature of a curve (not the formula, what does it actually mean conceptually)? Secondly, I am confused about how one can figure out when a curve would have the maximum curvature. I was told it is when the derivative of the curvature function (k(x)) = 0. But, I don't understand the concept/reason behind it.
In the book I am using there are more than one definitions for curvature. Some of them are: