Let's say we have two lines. I want to compare which line is more "curved" over the same interval. For example, let's say:
$f1(x) = x^2$
$f2(x) = sin(3x)$
Over the interval x = [0, 1], it is arguable, that f2(x) is more "curved". What are some metrics to measure which two lines are more curved? Curved can be a function of range(f(x)), how much f(x) changes direction, etc...
Are there any good ones out there?