Vector functions - Determine maximum curvature

Question

Determine the maximum curvature for the graph of

​f(x)=3ln(7x).

The maximum curvature is

? at x= ?

I need the maximum curvature and the x=?

Answer 1

Curvature is defined as k(x) = y''/(1+y'²)^3/2 . Usually, people are interested in mins or maxes of curvature so they take the derivative and set it to zero. This results in a polynomial of the first three derivatives of y:

P(x) = y'''(1+y'²) - 3y'(y'')²

You find the zeros of this equation in order to find the extrema.