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Find a function whose graph has given properties

Let f be a function such that the points P_0 = (0,1) and P_1 = (1,0) are on the graph of f. Assume that for every point P = (x,y) on the graph of f, the graph is above the line segment joining P_0 to P. Further, assume that the area A(x) of the region bounded by the graph of f and the line segment is x^3. Find a formula for the function f.


Incomplete.

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