Explaination of Curvature

by prace
Tags: curvature, explaination
 P: 102 1. The problem statement, all variables and given/known data Find the curvature of y = x³ 2. Relevant equations $$k(x) = \frac{f"(x)}{[1+(f'(x))²]^{3/2}$$ 3. The attempt at a solution $$k(x) = \frac{6x}{(1+9x^4)^{3/2}$$ I got the answer numerically, but I am looking for an explaination of the graph itself. I chose a relatively easy function in hopes that it would be easy to explain. Any help would be great. Please see the image below: The red curve represents the original function, and the blue curve represents the curvature. Could someone please explain how the blue curve represents the curvature? I just can't see how they are related. ** Sorry, I can't seem to get the LaTeX correct, but I will work on it and get the right equations on there. For the time being, I have them posted on the graph itself ** thanks