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Math problem thread

Name: Anonymous 2009-10-05 10:23

Find all differentiable functions f: R -> R+ for which the following is true: f'(x) = f(f(x))

Name: Anonymous 2009-10-08 22:51

>>10
Place the island in the Cartesian plane with the coconut tree on (0,0) and the banana tree on (a,0), a>0. If the boulder is on (x,y), the first instructions correspond to rotate (x,y) -90º around the origin, which sends it to (y,-x) where you place the coconut. Now go back to the boulder, the second part of the instructions is rotating (x,y) +90º around (0,a), leaving you in (a-y,x-a). The midpoint between (y,-x) and (a-y,x-a) is (a/2,-a/2) which doesn't depend of (x,y). Showing that the location of the boulder is not relevant.

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