of the
Week
| |
Problem
of the Week |
Consider the graph of f(x) = x2. See the figure on the
right. 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 f(x) = xn, 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.
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