Draft:Bpow58

Consider the graph of <m>f(x) = x^2</m>. Imagine a circle of radius 1 rolling along the x-axis toward the origin until the circle just comes into contact with the graph. Where does the center (a,b) of the circle come to rest?

For the more adventurous, consider the same question for the function <m>f(x) = x^n</m>, for n a positive real number.

For the truly death defying, consider the same question for an arbitrary increasing function having second derivative of constant sign.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.